I have today finished examining the Leyland numbers from 1000800 digits to 1000899 digits and have found no PRPs therein. This adds to my previous search of 1000900 digits to 1000999 digits completed 26 Jan 2024 wherein I found three PRPs. At nine to ten months per search, I am not anxious to try another such interval. Yesterday was the ninth (year) anniversary of my very first Leyland-prime find. That's a long time to be obsessed with the task. I'm going to take a breather.
Friday, October 04, 2024
Thursday, October 03, 2024
Éric Angelini (1951-2024)
Pascale SCHOENMAECKERS,
son épouse,
Cécile ANGELINI,
Lorenzo ANGELINI et Marie LE HENAFF,
ses enfants et sa belle-fille,
Domenico ANGELINI et Monica ANGELINI,
Catherine ANGELINI,
Letizia ANGELINI et Henri DEFRANCHI,
Marina ANGELINI et Éric VAN NEROM,
son frère et ses soeurs,
Bidè,
son compère,
Les familles ANGELINI et apparentées,
ont la tristesse d’annoncer le décès de
MONSIEUR
Éric ANGELINI
né à Ostende le 12 septembre 1951
et décédé à Uccle le 27 septembre 2024.
Le service, suivi de l’inhumation au cimetière d’Ixelles,
aura lieu dans l’église Sainte-Anne à Uccle
le JEUDI 3 OCTOBRE 2024, à 10 h 30.
La famille y recevra les condoléances dès 10 heures.
Après avoir joué 1. e4, Éric aurait relevé que
le présent avis, qui tient lieu de faire-part,
comporte six cent septante-cinq signes jusqu’ici.
The above transliterated copy of the original obituary allows for two ligatures to be treated each as two "signes" in order to make the self-referential closing assertion true. Éric's final Cinquante signes article just misses Michael Branicky's (late Sep. 27) emailed response:
1 [length 0]
2 [length 8]
-> 2^2 = 4
-> 4^2 = 16
-> 1^2 + 6^2 = 37
-> 37^2 = 1369
-> 1^2 + 369^2 = 136162
-> 1^2 + 36^2 + 16^2 + 2^2 = 1557
-> 1^2 + 5^2 + 5^2 + 7^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
3 [length 7]
-> 3^2 = 9
-> 9^2 = 81
-> 81^2 = 6561
-> 6^2 + 56^2 + 1^2 = 3173
-> 3^2 + 1^2 + 7^2 + 3^2 = 68
-> 6^2 + 8^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
4 [length 7]
-> 4^2 = 16
-> 1^2 + 6^2 = 37
-> 37^2 = 1369
-> 1^2 + 369^2 = 136162
-> 1^2 + 36^2 + 16^2 + 2^2 = 1557
-> 1^2 + 5^2 + 5^2 + 7^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
5 [length 7]
-> 5^2 = 25
-> 25^2 = 625
-> 62^2 + 5^2 = 3869
-> 3^2 + 869^2 = 755170
-> 755^2 + 17^2 + 0^2 = 570314
-> 5^2 + 7^2 + 0^2 + 3^2 + 1^2 + 4^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
6 [length 6]
-> 6^2 = 36
-> 36^2 = 1296
-> 1296^2 = 1679616
-> 1679616^2 = 2821109907456
-> 28^2 + 21^2 + 1^2 + 0^2 + 9^2 + 9^2 + 0^2 + 74^2 + 56^2 = 10000
-> 1^2 + 0^2 + 0^2 + 0^2 + 0^2 = 1
7 [length 5]
-> 7^2 = 49
-> 4^2 + 9^2 = 97
-> 9^2 + 7^2 = 130
-> 1^2 + 3^2 + 0^2 = 10
-> 1^2 + 0^2 = 1
8 [length 5]
-> 8^2 = 64
-> 64^2 = 4096
-> 40^2 + 9^2 + 6^2 = 1717
-> 1^2 + 7^2 + 1^2 + 7^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
9 [length 6]
-> 9^2 = 81
-> 81^2 = 6561
-> 6^2 + 56^2 + 1^2 = 3173
-> 3^2 + 1^2 + 7^2 + 3^2 = 68
-> 6^2 + 8^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
10 [length 1]
-> 1^2 + 0^2 = 1
11 [length 6]
-> 11^2 = 121
-> 12^2 + 1^2 = 145
-> 1^2 + 45^2 = 2026
-> 2^2 + 0^2 + 26^2 = 680
-> 6^2 + 8^2 + 0^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
12 [length 6]
-> 12^2 = 144
-> 1^2 + 44^2 = 1937
-> 1^2 + 9^2 + 37^2 = 1451
-> 1^2 + 4^2 + 51^2 = 2618
-> 26^2 + 18^2 = 1000
-> 1^2 + 0^2 + 0^2 + 0^2 = 1
13 [length 2]
-> 1^2 + 3^2 = 10
-> 1^2 + 0^2 = 1
14 [length 6]
-> 1^2 + 4^2 = 17
-> 17^2 = 289
-> 289^2 = 83521
-> 8^2 + 3^2 + 5^2 + 2^2 + 1^2 = 103
-> 1^2 + 0^2 + 3^2 = 10
-> 1^2 + 0^2 = 1
15 [length 6]
-> 15^2 = 225
-> 225^2 = 50625
-> 5^2 + 0^2 + 625^2 = 390650
-> 390^2 + 65^2 + 0^2 = 156325
-> 1^2 + 5^2 + 6^2 + 3^2 + 2^2 + 5^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
16 [length 6]
-> 1^2 + 6^2 = 37
-> 37^2 = 1369
-> 1^2 + 369^2 = 136162
-> 1^2 + 36^2 + 16^2 + 2^2 = 1557
-> 1^2 + 5^2 + 5^2 + 7^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
17 [length 5]
-> 17^2 = 289
-> 289^2 = 83521
-> 8^2 + 3^2 + 5^2 + 2^2 + 1^2 = 103
-> 1^2 + 0^2 + 3^2 = 10
-> 1^2 + 0^2 = 1
18 [length 6]
-> 1^2 + 8^2 = 65
-> 65^2 = 4225
-> 4^2 + 225^2 = 50641
-> 50^2 + 641^2 = 413381
-> 4^2 + 1^2 + 3^2 + 3^2 + 8^2 + 1^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
19 [length 4]
-> 1^2 + 9^2 = 82
-> 8^2 + 2^2 = 68
-> 6^2 + 8^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
20 [length 7]
-> 20^2 = 400
-> 40^2 + 0^2 = 1600
-> 1^2 + 60^2 + 0^2 = 3601
-> 3601^2 = 12967201
-> 12967201^2 = 168148301774401
-> 16^2 + 8^2 + 1^2 + 48^2 + 3^2 + 0^2 + 17^2 + 74^2 + 40^2 + 1^2 = 10000
-> 1^2 + 0^2 + 0^2 + 0^2 + 0^2 = 1
21 [length 6]
-> 21^2 = 441
-> 4^2 + 41^2 = 1697
-> 1^2 + 6^2 + 9^2 + 7^2 = 167
-> 1^2 + 6^2 + 7^2 = 86
-> 8^2 + 6^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
22 [length 6]
-> 2^2 + 2^2 = 8
-> 8^2 = 64
-> 64^2 = 4096
-> 40^2 + 9^2 + 6^2 = 1717
-> 1^2 + 7^2 + 1^2 + 7^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
23 [length 3]
-> 2^2 + 3^2 = 13
-> 1^2 + 3^2 = 10
-> 1^2 + 0^2 = 1
24 [length 6]
-> 24^2 = 576
-> 57^2 + 6^2 = 3285
-> 3285^2 = 10791225
-> 10^2 + 7^2 + 9^2 + 1^2 + 2^2 + 25^2 = 860
-> 8^2 + 6^2 + 0^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
25 [length 6]
-> 25^2 = 625
-> 62^2 + 5^2 = 3869
-> 3^2 + 869^2 = 755170
-> 755^2 + 17^2 + 0^2 = 570314
-> 5^2 + 7^2 + 0^2 + 3^2 + 1^2 + 4^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
26 [length 6]
-> 26^2 = 676
-> 67^2 + 6^2 = 4525
-> 4^2 + 525^2 = 275641
-> 2^2 + 7^2 + 564^2 + 1^2 = 318150
-> 3^2 + 1^2 + 8^2 + 1^2 + 5^2 + 0^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
27 [length 5]
-> 27^2 = 729
-> 729^2 = 531441
-> 5^2 + 3^2 + 1^2 + 4^2 + 4^2 + 1^2 = 68
-> 6^2 + 8^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
28 [length 3]
-> 2^2 + 8^2 = 68
-> 6^2 + 8^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
29 [length 6]
-> 2^2 + 9^2 = 85
-> 85^2 = 7225
-> 7^2 + 2^2 + 2^2 + 5^2 = 82
-> 8^2 + 2^2 = 68
-> 6^2 + 8^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
30 [length 6]
-> 30^2 = 900
-> 90^2 + 0^2 = 8100
-> 810^2 + 0^2 = 656100
-> 6^2 + 5^2 + 610^2 + 0^2 = 372161
-> 3^2 + 7^2 + 2^2 + 1^2 + 6^2 + 1^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
31 [length 2]
-> 3^2 + 1^2 = 10
-> 1^2 + 0^2 = 1
32 [length 3]
-> 3^2 + 2^2 = 13
-> 1^2 + 3^2 = 10
-> 1^2 + 0^2 = 1
33 [length 6]
-> 33^2 = 1089
-> 1^2 + 0^2 + 89^2 = 7922
-> 7^2 + 922^2 = 850133
-> 85013^2 + 3^2 = 7227210178
-> 7^2 + 2^2 + 27^2 + 2^2 + 10^2 + 1^2 + 7^2 + 8^2 = 1000
-> 1^2 + 0^2 + 0^2 + 0^2 = 1
34 [length 5]
-> 34^2 = 1156
-> 1^2 + 15^2 + 6^2 = 262
-> 26^2 + 2^2 = 680
-> 6^2 + 8^2 + 0^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
35 [length 6]
-> 3^2 + 5^2 = 34
-> 34^2 = 1156
-> 1^2 + 15^2 + 6^2 = 262
-> 26^2 + 2^2 = 680
-> 6^2 + 8^2 + 0^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
36 [length 5]
-> 36^2 = 1296
-> 1296^2 = 1679616
-> 1679616^2 = 2821109907456
-> 28^2 + 21^2 + 1^2 + 0^2 + 9^2 + 9^2 + 0^2 + 74^2 + 56^2 = 10000
-> 1^2 + 0^2 + 0^2 + 0^2 + 0^2 = 1
37 [length 5]
-> 37^2 = 1369
-> 1^2 + 369^2 = 136162
-> 1^2 + 36^2 + 16^2 + 2^2 = 1557
-> 1^2 + 5^2 + 5^2 + 7^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
38 [length 5]
-> 38^2 = 1444
-> 144^2 + 4^2 = 20752
-> 207^2 + 52^2 = 45553
-> 4^2 + 5^2 + 5^2 + 5^2 + 3^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
39 [length 4]
-> 39^2 = 1521
-> 1^2 + 5^2 + 2^2 + 1^2 = 31
-> 3^2 + 1^2 = 10
-> 1^2 + 0^2 = 1
40 [length 6]
-> 40^2 = 1600
-> 1^2 + 60^2 + 0^2 = 3601
-> 3601^2 = 12967201
-> 12967201^2 = 168148301774401
-> 16^2 + 8^2 + 1^2 + 48^2 + 3^2 + 0^2 + 17^2 + 74^2 + 40^2 + 1^2 = 10000
-> 1^2 + 0^2 + 0^2 + 0^2 + 0^2 = 1
41 [length 6]
-> 4^2 + 1^2 = 17
-> 17^2 = 289
-> 289^2 = 83521
-> 8^2 + 3^2 + 5^2 + 2^2 + 1^2 = 103
-> 1^2 + 0^2 + 3^2 = 10
-> 1^2 + 0^2 = 1
42 [length 6]
-> 42^2 = 1764
-> 1^2 + 7^2 + 6^2 + 4^2 = 102
-> 102^2 = 10404
-> 1^2 + 0^2 + 404^2 = 163217
-> 1^2 + 6^2 + 3^2 + 2^2 + 1^2 + 7^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
43 [length 6]
-> 43^2 = 1849
-> 1^2 + 8^2 + 49^2 = 2466
-> 2^2 + 466^2 = 217160
-> 2^2 + 1^2 + 7^2 + 16^2 + 0^2 = 310
-> 3^2 + 1^2 + 0^2 = 10
-> 1^2 + 0^2 = 1
44 [length 4]
-> 4^2 + 4^2 = 32
-> 3^2 + 2^2 = 13
-> 1^2 + 3^2 = 10
-> 1^2 + 0^2 = 1
45 [length 6]
-> 45^2 = 2025
-> 20^2 + 25^2 = 1025
-> 10^2 + 2^2 + 5^2 = 129
-> 1^2 + 2^2 + 9^2 = 86
-> 8^2 + 6^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
46 [length 5]
-> 46^2 = 2116
-> 2116^2 = 4477456
-> 4^2 + 47^2 + 7^2 + 456^2 = 210210
-> 2^2 + 1^2 + 0^2 + 2^2 + 1^2 + 0^2 = 10
-> 1^2 + 0^2 = 1
47 [length 5]
-> 47^2 = 2209
-> 22^2 + 0^2 + 9^2 = 565
-> 5^2 + 6^2 + 5^2 = 86
-> 8^2 + 6^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
48 [length 5]
-> 48^2 = 2304
-> 230^2 + 4^2 = 52916
-> 5^2 + 29^2 + 16^2 = 1122
-> 1^2 + 1^2 + 2^2 + 2^2 = 10
-> 1^2 + 0^2 = 1
49 [length 4]
-> 4^2 + 9^2 = 97
-> 9^2 + 7^2 = 130
-> 1^2 + 3^2 + 0^2 = 10
-> 1^2 + 0^2 = 1
50 [length 6]
-> 50^2 = 2500
-> 2^2 + 50^2 + 0^2 = 2504
-> 25^2 + 0^2 + 4^2 = 641
-> 6^2 + 41^2 = 1717
-> 1^2 + 7^2 + 1^2 + 7^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
51 [length 6]
-> 51^2 = 2601
-> 2^2 + 60^2 + 1^2 = 3605
-> 3^2 + 605^2 = 366034
-> 366034^2 = 133980889156
-> 13^2 + 39^2 + 8^2 + 0^2 + 8^2 + 89^2 + 15^2 + 6^2 = 10000
-> 1^2 + 0^2 + 0^2 + 0^2 + 0^2 = 1
52 [length 5]
-> 52^2 = 2704
-> 2704^2 = 7311616
-> 731^2 + 1^2 + 6^2 + 1^2 + 6^2 = 534435
-> 5^2 + 3^2 + 4^2 + 4^2 + 3^2 + 5^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
53 [length 6]
-> 5^2 + 3^2 = 34
-> 34^2 = 1156
-> 1^2 + 15^2 + 6^2 = 262
-> 26^2 + 2^2 = 680
-> 6^2 + 8^2 + 0^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
54 [length 5]
-> 54^2 = 2916
-> 291^2 + 6^2 = 84717
-> 84^2 + 7^2 + 1^2 + 7^2 = 7155
-> 7^2 + 1^2 + 5^2 + 5^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
55 [length 5]
-> 55^2 = 3025
-> 302^2 + 5^2 = 91229
-> 9^2 + 12^2 + 2^2 + 9^2 = 310
-> 3^2 + 1^2 + 0^2 = 10
-> 1^2 + 0^2 = 1
56 [length 6]
-> 5^2 + 6^2 = 61
-> 61^2 = 3721
-> 3721^2 = 13845841
-> 1^2 + 38^2 + 4^2 + 58^2 + 4^2 + 1^2 = 4842
-> 4^2 + 8^2 + 4^2 + 2^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
57 [length 4]
-> 57^2 = 3249
-> 324^2 + 9^2 = 105057
-> 1^2 + 0^2 + 5^2 + 0^2 + 5^2 + 7^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
58 [length 5]
-> 58^2 = 3364
-> 3364^2 = 11316496
-> 113^2 + 16^2 + 4^2 + 9^2 + 6^2 = 13158
-> 1^2 + 3^2 + 1^2 + 5^2 + 8^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
59 [length 4]
-> 59^2 = 3481
-> 34^2 + 8^2 + 1^2 = 1221
-> 1^2 + 2^2 + 2^2 + 1^2 = 10
-> 1^2 + 0^2 = 1
60 [length 6]
-> 6^2 + 0^2 = 36
-> 36^2 = 1296
-> 1296^2 = 1679616
-> 1679616^2 = 2821109907456
-> 28^2 + 21^2 + 1^2 + 0^2 + 9^2 + 9^2 + 0^2 + 74^2 + 56^2 = 10000
-> 1^2 + 0^2 + 0^2 + 0^2 + 0^2 = 1
61 [length 5]
-> 61^2 = 3721
-> 3721^2 = 13845841
-> 1^2 + 38^2 + 4^2 + 58^2 + 4^2 + 1^2 = 4842
-> 4^2 + 8^2 + 4^2 + 2^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
62 [length 5]
-> 62^2 = 3844
-> 3844^2 = 14776336
-> 14776^2 + 3^2 + 3^2 + 6^2 = 218330230
-> 2^2 + 1^2 + 8^2 + 3^2 + 3^2 + 0^2 + 2^2 + 3^2 + 0^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
63 [length 5]
-> 63^2 = 3969
-> 3^2 + 969^2 = 938970
-> 9^2 + 3^2 + 89^2 + 7^2 + 0^2 = 8060
-> 8^2 + 0^2 + 6^2 + 0^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
64 [length 4]
-> 64^2 = 4096
-> 40^2 + 9^2 + 6^2 = 1717
-> 1^2 + 7^2 + 1^2 + 7^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
65 [length 5]
-> 65^2 = 4225
-> 4^2 + 225^2 = 50641
-> 50^2 + 641^2 = 413381
-> 4^2 + 1^2 + 3^2 + 3^2 + 8^2 + 1^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
66 [length 4]
-> 66^2 = 4356
-> 4^2 + 3^2 + 5^2 + 6^2 = 86
-> 8^2 + 6^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
67 [length 6]
-> 6^2 + 7^2 = 85
-> 85^2 = 7225
-> 7^2 + 2^2 + 2^2 + 5^2 = 82
-> 8^2 + 2^2 = 68
-> 6^2 + 8^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
68 [length 2]
-> 6^2 + 8^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
69 [length 5]
-> 6^2 + 9^2 = 117
-> 117^2 = 13689
-> 13689^2 = 187388721
-> 18^2 + 7^2 + 3^2 + 8^2 + 8^2 + 7^2 + 21^2 = 1000
-> 1^2 + 0^2 + 0^2 + 0^2 = 1
70 [length 5]
-> 7^2 + 0^2 = 49
-> 4^2 + 9^2 = 97
-> 9^2 + 7^2 = 130
-> 1^2 + 3^2 + 0^2 = 10
-> 1^2 + 0^2 = 1
71 [length 5]
-> 71^2 = 5041
-> 5^2 + 0^2 + 41^2 = 1706
-> 1^2 + 7^2 + 0^2 + 6^2 = 86
-> 8^2 + 6^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
72 [length 6]
-> 72^2 = 5184
-> 51^2 + 8^2 + 4^2 = 2681
-> 2681^2 = 7187761
-> 7^2 + 1^2 + 8^2 + 77^2 + 6^2 + 1^2 = 6080
-> 6^2 + 0^2 + 8^2 + 0^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
73 [length 5]
-> 73^2 = 5329
-> 5^2 + 32^2 + 9^2 = 1130
-> 11^2 + 3^2 + 0^2 = 130
-> 1^2 + 3^2 + 0^2 = 10
-> 1^2 + 0^2 = 1
74 [length 4]
-> 74^2 = 5476
-> 54^2 + 7^2 + 6^2 = 3001
-> 3^2 + 0^2 + 0^2 + 1^2 = 10
-> 1^2 + 0^2 = 1
75 [length 5]
-> 7^2 + 5^2 = 74
-> 74^2 = 5476
-> 54^2 + 7^2 + 6^2 = 3001
-> 3^2 + 0^2 + 0^2 + 1^2 = 10
-> 1^2 + 0^2 = 1
76 [length 5]
-> 76^2 = 5776
-> 5776^2 = 33362176
-> 33^2 + 362^2 + 1^2 + 7^2 + 6^2 = 132219
-> 1^2 + 3^2 + 2^2 + 2^2 + 1^2 + 9^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
77 [length 4]
-> 77^2 = 5929
-> 592^2 + 9^2 = 350545
-> 3^2 + 5^2 + 0^2 + 5^2 + 4^2 + 5^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
78 [length 4]
-> 7^2 + 8^2 = 113
-> 11^2 + 3^2 = 130
-> 1^2 + 3^2 + 0^2 = 10
-> 1^2 + 0^2 = 1
79 [length 3]
-> 7^2 + 9^2 = 130
-> 1^2 + 3^2 + 0^2 = 10
-> 1^2 + 0^2 = 1
80 [length 5]
-> 8^2 + 0^2 = 64
-> 64^2 = 4096
-> 40^2 + 9^2 + 6^2 = 1717
-> 1^2 + 7^2 + 1^2 + 7^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
81 [length 5]
-> 81^2 = 6561
-> 6^2 + 56^2 + 1^2 = 3173
-> 3^2 + 1^2 + 7^2 + 3^2 = 68
-> 6^2 + 8^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
82 [length 3]
-> 8^2 + 2^2 = 68
-> 6^2 + 8^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
83 [length 5]
-> 83^2 = 6889
-> 688^2 + 9^2 = 473425
-> 4734^2 + 25^2 = 22411381
-> 2^2 + 2^2 + 4^2 + 1^2 + 1^2 + 3^2 + 8^2 + 1^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
84 [length 5]
-> 84^2 = 7056
-> 7^2 + 0^2 + 56^2 = 3185
-> 318^2 + 5^2 = 101149
-> 1^2 + 0^2 + 1^2 + 1^2 + 4^2 + 9^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
85 [length 5]
-> 85^2 = 7225
-> 7^2 + 2^2 + 2^2 + 5^2 = 82
-> 8^2 + 2^2 = 68
-> 6^2 + 8^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
86 [length 2]
-> 8^2 + 6^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
87 [length 4]
-> 8^2 + 7^2 = 113
-> 11^2 + 3^2 = 130
-> 1^2 + 3^2 + 0^2 = 10
-> 1^2 + 0^2 = 1
88 [length 4]
-> 88^2 = 7744
-> 7^2 + 7^2 + 4^2 + 4^2 = 130
-> 1^2 + 3^2 + 0^2 = 10
-> 1^2 + 0^2 = 1
89 [length 5]
-> 8^2 + 9^2 = 145
-> 1^2 + 45^2 = 2026
-> 2^2 + 0^2 + 26^2 = 680
-> 6^2 + 8^2 + 0^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
90 [length 5]
-> 90^2 = 8100
-> 810^2 + 0^2 = 656100
-> 6^2 + 5^2 + 610^2 + 0^2 = 372161
-> 3^2 + 7^2 + 2^2 + 1^2 + 6^2 + 1^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
91 [length 4]
-> 9^2 + 1^2 = 82
-> 8^2 + 2^2 = 68
-> 6^2 + 8^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
92 [length 5]
-> 92^2 = 8464
-> 8464^2 = 71639296
-> 7^2 + 1^2 + 6^2 + 39^2 + 29^2 + 6^2 = 2484
-> 2^2 + 4^2 + 8^2 + 4^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
93 [length 5]
-> 93^2 = 8649
-> 8^2 + 649^2 = 421265
-> 4^2 + 2^2 + 1^2 + 2^2 + 6^2 + 5^2 = 86
-> 8^2 + 6^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
94 [length 4]
-> 9^2 + 4^2 = 97
-> 9^2 + 7^2 = 130
-> 1^2 + 3^2 + 0^2 = 10
-> 1^2 + 0^2 = 1
95 [length 5]
-> 95^2 = 9025
-> 9025^2 = 81450625
-> 81^2 + 4^2 + 506^2 + 2^2 + 5^2 = 262642
-> 2^2 + 6^2 + 2^2 + 6^2 + 4^2 + 2^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
96 [length 5]
-> 9^2 + 6^2 = 117
-> 117^2 = 13689
-> 13689^2 = 187388721
-> 18^2 + 7^2 + 3^2 + 8^2 + 8^2 + 7^2 + 21^2 = 1000
-> 1^2 + 0^2 + 0^2 + 0^2 = 1
97 [length 3]
-> 9^2 + 7^2 = 130
-> 1^2 + 3^2 + 0^2 = 10
-> 1^2 + 0^2 = 1
98 [length 5]
-> 9^2 + 8^2 = 145
-> 1^2 + 45^2 = 2026
-> 2^2 + 0^2 + 26^2 = 680
-> 6^2 + 8^2 + 0^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
99 [length 5]
-> 99^2 = 9801
-> 9^2 + 801^2 = 641682
-> 6416^2 + 8^2 + 2^2 = 41165124
-> 4^2 + 1^2 + 1^2 + 6^2 + 5^2 + 1^2 + 2^2 + 4^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
100 [length 1]
-> 1^2 + 0^2 + 0^2 = 1
Friday, September 20, 2024
Friday, September 13, 2024
Recycling
One of the pastimes of living where we live is to curtain twitch a credible comprehension of human behaviour, such as it is.
Thursday, September 05, 2024
Unknown Havermann
I ran into my older sister's genealogy post on an Unknown Havermann yesterday and I was wondering how it ever came to this. Back in 2010 we had a brief email discussion on the matter (I've made some of my reply-text bold for emphasis):
16 Nov 2010
I read with interest your blog on our family tree. I am amazed that you were able to go back that far. Question: Generation V: Heinrich (living with his mother in 1900) +
[The Generation-V link is a 2022-updated page. The + is a date-of-death marker. In 2010, I did not yet know that date. I have a Neheim1900 excerpt that lists only some family names.]
I have a Heinrich who was a child of Sette – born: Jan.30/1901; died: Feb.26/1922 which seems to be at odds with your information that he was a child of Heinrich Havermann and Maria Messelke. Perhaps we are talking about another Heinrich?
17 Nov 2010 reply
My Heinrich came directly from dad's Stammbuch. I had scanned a copy of it for my computer but I have since lost that file because of a hard drive failure a couple of years ago. You will have to look at the original (assuming it wasn't thrown out). The residents-living-in-Neheim-in-1900 list basically confirms the existence of that person. He is old enough to be a Fabrikarbeiter and indeed, because his father died in 1876, he would have been at least 24 years old then.
18 Nov 2010
Thanks for your email clarifying my inquiry. I do have the "Ahnenpass". This seems to be a booklet that belonged to the relatives in Wattenscheid. Is this the same as the "Stammbuch" that you are referring to. I am willing to share the information with you if you want. Let me know.
18 Nov 2010 reply
[to part 1] Yes, that sounds like it. It does have Heinrich as a son of Heinrich, does it not?
[to part 2] No. I have all the information I need.
On my end, Heinrich wasn't an "unknown" (birthdate "estimated between 1844 and 1900"). He was Heinrich Anton, born 30 Jan 1876, three days before his father's death! Is it any wonder that his mother named him after his father? He died 26 Feb 1922. I don't know if he ever married or had children, but my sister listed a son, Heinrich (30 Jan 1901 - 26 Feb 1922), which perversely mirrors the actual Heinrich's particulars except for the year of birth. My sister suggested that Heinrich might have been a child of Sette but that would have made him a Rademacher, not a Havermann (an actual Heinrich Rademacher was 1907-1945).
I'm having difficulty finding a lot of my original sources for all this. Heinrich Anton's birth year of 1876 is in the Stadt- und Landständearchiv im Kloster Wedinghausen (Alphabetisches Register, 1874 - 1879). I'm pretty sure that I had found a reference to his Helden Friedhof burial in a book that corroborates his birth year but I've been unable to re-discover it.
Anyways, I just wanted this on the record in case some future researcher is confused by the geni.com misinformation. As mentioned in a previous blog, I have an extended Havermann family text chart and, as well, a slightly more limited pictorial chart. But beware. The "chesswanks" links are files on my computer and will likely disappear after my death.
Sunday, September 01, 2024
Goodbye Netflix, hello YouTube Premium
Today is the last day of my long-time (since April 2013) Netflix subscription and the first day of my new YouTube Premium subscription for which I'll be paying $5.64 less per month after my one-month-free trial.
Thursday, August 29, 2024
The pore structure of Clostridium perfringens epsilon toxin
 |
| [article] BioMoleculePlot3D (ribbons) in Wolfram 14.1: click to enlarge |
Friday, August 09, 2024
Alphabetizing the integers
Last month I wrote an article called "Integers, in alphabetical order" that illustrated my then-obsession with the topic. In February 1981, Ross Eckler had an article called "Alphabetizing the integers" (in the magazine Word Ways) that loosely anticipated my exploration.
On page 20 of his article, Eckler notes Philip Cohen's approach to the "Bergerson" problem (find the fixed points for integers 1 to n):
one one one four five five five eight eight
two three one four four four five five
two three one one one four four
two three six seven one nine
two three six seven one
two three six seven
two three six
two three
two
The number of fixed-point counts leads us to OEIS sequence A340671, which provides the actual fixed points in one of the links. Eckler gives us the list-sizes which produce matches for the first twenty integers. I have extended this listing to 100000 integers here. Eckler then notes that 3 appears (I am paraphrasing) in A340671 at positions 13 and 31 and asks for additional values. The third occurrence is at position 201 (then 203, 204, 208, ...). He didn't ask for a first 4, 5, 6, ... appearance as these were clearly beyond his realm of realizability at the time. But here they are:
1 1
2 2
3 13
4 202
5 213
6 2202
7 2213
8 14475
9 233164
10 320200
11 449694
12 2450694
13 4367488
14 4580804
15 4580824
The listing is for the first appearance of 1 to 15, giving the position/index at which it occurs. Michael Branicky found #12 on July 7. I determined #13 to #15 yesterday. The fixed points are added here.
Tuesday, July 30, 2024
Fun with digital roots
Éric Angelini's most recent blog is here. I was sufficiently intrigued with his challenge to find larger primes than his 20248751248751248751248751248751248751248751248751 that I gave it a go:
z(41) = 20 grows into z(89), Éric's 50-digit prime.
z(91) = 22 grows into z(280), a 191-digit prime.
z(300) = 35 grows into z(1064), a 766-digit prime.
z(3740) = 238 grows into z(d+3737), a d-digit (>145000) prime.
Up to this point, we have 151 primes in Z. Their positions/indices are: 2, 3, 4, 20, 21, 23, 26, 29, 31, 34, 37, 38, 40, 89, 280, 281, 284, 287, 290, 291, 293, 296, 299, 1064, 1066, 1073, 1078, 1079, 1081, 1084, 1085, 1144, 1147, 1170, 1171, 1184, 1221, 1262, 1263, 1265, 1268, 1271, 1278, 1280, 1287, 1616, 1617, 1619, 1660, 1665, 1698, 1700, 1703, 1706, 1707, 1712, 1719, 1721, 1724, 1729, 1784, 1787, 1789, 1792, 1897, 1899, 1914, 1919, 1920, 1922, 1965, 1972, 1973, 1978, 1983, 1986, 1993, 1998, 2001, 2022, 2043, 2045, 2064, 2075, 2076, 2097, 2100, 2103, 2104, 2106, 2109, 2112, 2115, 2225, 2242, 2243, 2245, 2248, 2293, 2336, 2338, 2363, 2366, 2369, 2371, 2388, 2393, 2396, 2513, 2516, 2517, 2660, 2693, 2696, 2697, 2699, 2704, 2709, 2724, 2727, 2744, 2747, 2748, 2750, 2795, 2800, 2801, 2803, 2810, 3156, 3183, 3188, 3191, 3204, 3206, 3225, 3290, 3293, 3360, 3427, 3462, 3475, 3477, 3484, 3485, 3487, 3506, 3511, 3512, 3515, 3738. So we are looking for prime #152 (the next one). I've put an indexed file of Z (to 3752) here.
One might suppose that in the absence of a definite d, we cannot continue Z. Actually, assuming that d exists, we can. What we cannot do is assign indices to the continuation, unless one is ok with:
d+3738 239 (prime #153)
d+3739 240
d+3740 241 (prime #154)
d+3741 242
d+3742 2428
d+3743 24287
...
I've computed 11288 terms of this continuation but, in order to make the file size smaller, I have removed d+7693 to d+15024 from view. The file is here. The final term at the bottom (index d+15025) is prime #190, a 7348-digit prime.
Festival!
The 1967 Murray Lerner documentary using Newport Folk Festivals (1963-1966) footage was on Turner Classic Movies recently and Catherine engaged me last Saturday about some issues. Mostly who some of the artists were. That's because TCM played the damned thing without subtitles, which is egregious.
Antti Alanen's 2017 blog post was a big help for its ordered listing but, as I watched the film myself, I realized that there were a number of deficiencies that were not being helped by simply Googling the Net. Eventually I looked for an .srt file for the movie and, upon finding one, realized that even though the text was crap, I could edit it to make it more presentable. Meaning that I couldn't actually see the subtitles on a copy of film, so I just organized it in a manner where a printed copy would be a decent adjunct for anyone watching an unsubtitled version of Festival.
00:00:37.121 --> 00:00:41.334 Jim Kweskin & the Jug Band: "Hannah Won't You Open That Door"
00:01:52.405 --> 00:01:54.865 Mel Lyman
00:02:25.896 --> 00:02:28.232 Jim Kweskin
00:02:38.034 --> 00:02:40.619 Fritz Richmond
00:03:36.133 --> 00:03:40.304 Joe Patterson: untitled quill instrumental
00:06:41.819 --> 00:06:46.198 Peter, Paul and Mary: "Come and Go With Me"
00:08:21.669 --> 00:08:25.005 voice of Peter Yarrow
00:08:51.281 --> 00:08:54.326 Peter, Paul and Mary: "If I Had a Hammer"
00:11:01.370 --> 00:11:05.165 The Sacred Harp Singers: "Rocky Road"
00:11:12.297 --> 00:11:15.300 voice of Pete Seeger
00:12:11.481 --> 00:12:15.485 The Georgia Sea Island Singers & Friends
00:12:15.569 --> 00:12:18.572 "Since I Lay My Burden Down"
00:13:00.739 --> 00:13:04.201 The Blue Ridge Mountain Dancers: clog dance
00:13:04.284 --> 00:13:08.789 accompanied by Pappy Clayton McMichen, Mike Seeger, Pete Seeger
00:15:24.341 --> 00:15:27.761 voice of Pete Seeger
00:15:36.853 --> 00:15:41.525 Tex Logan & The Lilly Brothers: "Black Mountain Rag"
00:15:46.780 --> 00:15:49.032 Taj Mahal
00:16:34.327 --> 00:16:37.998 Tex Logan & The Lilly Brothers
00:17:13.742 --> 00:17:16.369 "Green Corn"
00:17:16.453 --> 00:17:19.623 Pete Seeger, with Mel Lyman & Jim Kweskin
00:18:31.152 --> 00:18:34.572 voice of Tom Paxton
00:18:51.965 --> 00:18:55.969 Buffy St. Marie: "Cod'ine"
00:21:41.301 --> 00:21:45.638 Spider John Koerner: "Crazy Fool"
00:22:08.411 --> 00:22:12.123 Pete Seeger: "Deep Blue Sea"
00:22:33.937 --> 00:22:37.982 Odetta: "Carry It Back to Rosie"
00:23:25.446 --> 00:23:29.659 Joan Baez & Peter Yarrow: "Go Tell Aunt Rhody"
00:25:25.358 --> 00:25:29.112 voice of Peter Yarrow
00:25:59.559 --> 00:26:02.979 Joan Baez: "Mary Hamilton"
00:28:26.789 --> 00:28:30.751 voice of Ronnie Gilbert
00:29:39.820 --> 00:29:43.282 voice of Peter Yarrow
Bob Dylan: "Mr. Tambourine Man"
00:29:51.791 --> 00:29:55.461 Bob Dylan: "All I Really Want to Do"
Joan Baez: "From Me to You"
00:36:46.163 --> 00:36:49.875 Joan Baez: "All My Trials"
00:38:02.197 --> 00:38:05.742 Peter, Paul and Mary: "Blowin’ in The Wind"
00:39:49.221 --> 00:39:53.642 Donovan: "And The War Drags On"
00:40:36.143 --> 00:40:39.980 Judy Collins: ”Turn, Turn, Turn”
00:41:21.188 --> 00:41:24.483 Fiddler Beers
00:42:04.064 --> 00:42:07.776 Donovan: "Ballad of a Crystal Man"
00:42:59.536 --> 00:43:03.498 Odetta: "I Be's Troubled"
00:44:01.681 --> 00:44:05.685 Peter, Paul and Mary: "The Times They Are A’Changing"
00:46:29.079 --> 00:46:33.333 Joan Baez & Donovan: "Colours"
00:49:39.602 --> 00:49:43.857 Fred McDowell: "61 Highway Blues"
00:50:28.401 --> 00:50:31.321 Fred McDowell
00:51:15.531 --> 00:51:19.702 Sonny Terry & Brownie McGhee: "Key to The Highway"
00:52:24.809 --> 00:52:28.104 voice of Mississippi John Hurt
00:52:43.661 --> 00:52:46.664 Mississippi John Hurt: "Candy Man"
00:53:42.720 --> 00:53:47.683 Bob Dylan rehearsing with The Paul Butterfield Blues Band
00:53:50.645 --> 00:53:53.481 Almeda Riddle
00:54:35.648 --> 00:54:38.234 Joe Patterson
00:54:48.870 --> 00:54:51.747 Eck Robertson
00:54:59.714 --> 00:55:03.468 Mrs. General Watson and Mrs. Ollie Gilbert
00:55:42.465 --> 00:55:46.636 Horton Barker: "Pretty Sally"
00:56:50.575 --> 00:56:54.537 Bob Dylan & The Paul Butterfield Blues Band*: "Maggie's Farm"
00:59:30.735 --> 00:59:33.612 Mike Bloomfield
01:00:14.987 --> 01:00:19.408 Lonnie & Ed Young Fife & Drums Corps: instrumental
01:01:53.127 --> 01:01:55.963 The Swan Silvertones: "Feed Me Jesus"
01:02:29.163 --> 01:02:32.958 The Staple Singers: ”Help Me Jesus”
01:03:19.254 --> 01:03:21.715 The Freedom Singers
01:03:21.799 --> 01:03:25.928 "Up Above My Head I Hear Music in the Air"
01:04:05.759 --> 01:04:09.471 voice of professor Willis James
01:04:39.668 --> 01:04:43.547 The Freedom Singers: "Ain’t Gonna Let Nobody Turn Me Round"
01:05:15.079 --> 01:05:19.124 Fannie Lou Hamer & Company: "Go Tell It on The Mountain"
01:05:35.849 --> 01:05:39.728 voice of Pete Seeger
01:05:51.198 --> 01:05:54.368 The Freedom Singers: "All God's Children"
01:06:55.179 --> 01:06:58.724 "We Shall Overcome"
01:07:53.904 --> 01:07:57.032 The Paul Butterfield Blues Band: "Born in Chicago"
01:09:10.981 --> 01:09:13.608 Mike Bloomfield
01:09:42.929 --> 01:09:45.932 Son House
01:11:44.050 --> 01:11:47.846 Son House: "Downhearted Blues"
01:13:37.163 --> 01:13:39.833 "Levee Camp Moan"
The Paul Butterfield Blues Band: instrumental
01:16:48.521 --> 01:16:52.358 Howlin' Wolf: "Howlin' for My Darling"
01:19:20.924 --> 01:19:25.386 Mimi & Richard Fariña: "Reno Nevada"
01:20:30.702 --> 01:20:34.706 "Pack Up Your Sorrows"
01:21:12.869 --> 01:21:15.621 Mel Lyman
01:21:27.508 --> 01:21:30.344 Spokes Mashiyane: flute instrumental
01:22:24.315 --> 01:22:28.277 Cousin Emmy: "Turkey in the Straw"
01:22:42.333 --> 01:22:45.336 Theodore Bikel: "Karabli"
01:23:36.137 --> 01:23:39.557 Judy Collins: "Anathea"
01:24:58.886 --> 01:25:03.224 Johnny Cash: "I Walk the Line"
01:25:48.728 --> 01:25:52.315 The Osborne Brothers: "Ruby"
01:27:34.375 --> 01:27:38.170 Joan Baez: "Farewell Angelina"
01:29:13.933 --> 01:29:17.728 Bob Dylan: "Mr. Tambourine Man"
01:31:33.947 --> 01:31:37.242 Peter, Paul and Mary
Paul Stookey: "On a Desert Island"
01:32:34.174 --> 01:32:37.386 "Rising of the Moon"
01:34:46.014 --> 01:34:49.268 Pete Seeger, et al., group finale: "Down by the Riverside"
* minus Paul Butterfield, plus Al Kooper & Barry Goldberg
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