Surrendered to Crazy

Surrounded by Crazy

Breather

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.

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

Encore

After last week's recycling, today is garbage pickup. We pay for one city-supplied bin, which is unlikely to remain upright (because of raccoons) if it is encumbered with food waste. When the truck arrived here, they took a photo before moving on.

Recycling

One of the pastimes of living where we live is to curtain twitch a credible comprehension of human behaviour, such as it is.

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.

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 $3.95 less per month after my one-month-free trial.

The pore structure of Clostridium perfringens epsilon toxin

[article] BioMoleculePlot3D (ribbons) in Wolfram 14.1: click to enlarge

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.