1 3960 threethousandni|nehundredsixty
2 13986 thirteenthousandni|nehundredeightysix
3 15368 fifteenthousandthre|ehundredsixtyeight
4 80547 eightythousandfive|hundredfortyseven
5 85740 eightyfivethousand|sevenhundredforty
6 111789 onehundredeleventhousan|dsevenhundredeightynine
7 111987 onehundredeleventhousan|dninehundredeightyseven
8 386048 threehundredeightysi|xthousandfortyeight
9 408649 fourhundredeightthous|andsixhundredfortynine
== fourhundredeightthousa|ndsixhundredfortynine
10 408946 fourhundredeightthous|andninehundredfortysix
== fourhundredeightthousa|ndninehundredfortysix
11 410699 fourhundredtenthousan|dsixhundredninetynine
12 410969 fourhundredtenthousan|dninehundredsixtynine
13 410996 fourhundredtenthousan|dninehundredninetysix
14 486014 fourhundredeightys|ixthousandfourteen
15 519487 fivehundrednineteenthous|andfourhundredeightyseven
== fivehundrednineteenthousa|ndfourhundredeightyseven
16 519784 fivehundrednineteenthous|andsevenhundredeightyfour
== fivehundrednineteenthousa|ndsevenhundredeightyfour
17 609408 sixhundredninethou|sandfourhundredeight
18 609804 sixhundredninethou|sandeighthundredfour
19 615430 sixhundredfifteenthou|sandfourhundredthirty
20 619814 sixhundrednineteenthou|sandeighthundredfourteen
21 629428 sixhundredtwentyninethou|sandfourhundredtwentyeight
22 629824 sixhundredtwentyninethou|sandeighthundredtwentyfour
23 639438 sixhundredthirtyninethou|sandfourhundredthirtyeight
24 639834 sixhundredthirtyninethou|sandeighthundredthirtyfour
25 649448 sixhundredfortyninethou|sandfourhundredfortyeight
26 649844 sixhundredfortyninethou|sandeighthundredfortyfour
27 659458 sixhundredfiftyninethou|sandfourhundredfiftyeight
28 659854 sixhundredfiftyninethou|sandeighthundredfiftyfour
29 669468 sixhundredsixtyninethou|sandfourhundredsixtyeight
30 669864 sixhundredsixtyninethou|sandeighthundredsixtyfour
31 679478 sixhundredseventyninethou|sandfourhundredseventyeight
32 679874 sixhundredseventyninethou|sandeighthundredseventyfour
33 686016 sixhundredeightys|ixthousandsixteen
34 688050 sixhundredeightye|ightthousandfifty
35 689400 sixhundredeightynin|ethousandfourhundred
36 689488 sixhundredeightyninethou|sandfourhundredeightyeight
37 689884 sixhundredeightyninethou|sandeighthundredeightyfour
38 696468 sixhundredninetysixthou|sandfourhundredsixtyeight
39 696864 sixhundredninetysixthou|sandeighthundredsixtyfour
40 697478 sixhundredninetyseventhou|sandfourhundredseventyeight
41 697874 sixhundredninetyseventhou|sandeighthundredseventyfour
42 699314 sixhundredninetyninetho|usandthreehundredfourteen
43 699498 sixhundredninetyninethou|sandfourhundredninetyeight
44 699894 sixhundredninetyninethou|sandeighthundredninetyfour
45 738045 sevenhundredthirtyei|ghtthousandfortyfive
46 740085 sevenhundredforty|thousandeightyfive
47 745080 sevenhundredforty|fivethousandeighty
48 769478 sevenhundredsixtyninethou|sandfourhundredseventyeight
49 769874 sevenhundredsixtyninethou|sandeighthundredseventyfour
50 786017 sevenhundredeightys|ixthousandseventeen
51 787016 sevenhundredeightys|eventhousandsixteen
52 796478 sevenhundredninetysixthou|sandfourhundredseventyeight
53 796874 sevenhundredninetysixthou|sandeighthundredseventyfour
54 804649 eighthundredfourthous|andsixhundredfortynine
== eighthundredfourthousa|ndsixhundredfortynine
55 804946 eighthundredfourthous|andninehundredfortysix
== eighthundredfourthousa|ndninehundredfortysix
56 847035 eighthundredfortysev|enthousandthirtyfive
57 875039 eighthundredseventyfi|vethousandthirtynine
58 906408 ninehundredsixthou|sandfourhundredeight
59 906804 ninehundredsixthou|sandeighthundredfour
60 916814 ninehundredsixteenthou|sandeighthundredfourteen
61 926428 ninehundredtwentysixthou|sandfourhundredtwentyeight
62 926824 ninehundredtwentysixthou|sandeighthundredtwentyfour
63 936438 ninehundredthirtysixthou|sandfourhundredthirtyeight
64 936834 ninehundredthirtysixthou|sandeighthundredthirtyfour
65 946448 ninehundredfortysixthou|sandfourhundredfortyeight
66 946844 ninehundredfortysixthou|sandeighthundredfortyfour
67 956458 ninehundredfiftysixthou|sandfourhundredfiftyeight
68 956854 ninehundredfiftysixthou|sandeighthundredfiftyfour
69 966468 ninehundredsixtysixthou|sandfourhundredsixtyeight
70 966864 ninehundredsixtysixthou|sandeighthundredsixtyfour
71 967478 ninehundredsixtyseventhou|sandfourhundredseventyeight
72 967874 ninehundredsixtyseventhou|sandeighthundredseventyfour
73 969314 ninehundredsixtyninetho|usandthreehundredfourteen
74 969498 ninehundredsixtyninethou|sandfourhundredninetyeight
75 969894 ninehundredsixtyninethou|sandeighthundredninetyfour
76 976478 ninehundredseventysixthou|sandfourhundredseventyeight
77 976874 ninehundredseventysixthou|sandeighthundredseventyfour
78 986019 ninehundredeightys|ixthousandnineteen
79 986488 ninehundredeightysixthou|sandfourhundredeightyeight
80 986884 ninehundredeightysixthou|sandeighthundredeightyfour
81 996314 ninehundredninetysixtho|usandthreehundredfourteen
82 996498 ninehundredninetysixthou|sandfourhundredninetyeight
83 996894 ninehundredninetysixthou|sandeighthundredninetyfour
84 1000107588 onebilliononehundredseventh|ousandfivehundredeightyeight
85 1000107885 onebilliononehundredseventh|ousandeighthundredeightyfive
86 1000307155 onebillionthreehundredseven|thousandonehundredfiftyfive
87 1000307551 onebillionthreehundredseven|thousandfivehundredfiftyone
88 1000700135 onebillionsevenhundredtho|usandonehundredthirtyfive
89 1000700531 onebillionsevenhundredtho|usandfivehundredthirtyone
90 1000701588 onebillionsevenhundredoneth|ousandfivehundredeightyeight
91 1000701885 onebillionsevenhundredoneth|ousandeighthundredeightyfive
92 1000703155 onebillionsevenhundredthree|thousandonehundredfiftyfive
93 1000703551 onebillionsevenhundredthree|thousandfivehundredfiftyone
94 1000710185 onebillionsevenhundredtent|housandonehundredeightyfive
95 1000710581 onebillionsevenhundredtent|housandfivehundredeightyone
96 1000722509 onebillionsevenhundredtwent|ytwothousandfivehundrednine
97 1000722905 onebillionsevenhundredtwent|ytwothousandninehundredfive
98 1000725209 onebillionsevenhundredtwent|yfivethousandtwohundrednine
99 1000725902 onebillionsevenhundredtwent|yfivethousandninehundredtwo
100 1000729205 onebillionsevenhundredtwent|yninethousandtwohundredfive
101 1000729502 onebillionsevenhundredtwent|yninethousandfivehundredtwo
102 1000733155 onebillionsevenhundredthirtyt|hreethousandonehundredfiftyfive
103 1000733551 onebillionsevenhundredthirtyt|hreethousandfivehundredfiftyone
104 1000817155 onebillioneighthundredsevente|enthousandonehundredfiftyfive
105 1000817551 onebillioneighthundredsevente|enthousandfivehundredfiftyone
106 1000879185 onebillioneighthundredseventyn|inethousandonehundredeightyfive
107 1000879581 onebillioneighthundredseventyn|inethousandfivehundredeightyone
108 2000307255 twobillionthreehundredseven|thousandtwohundredfiftyfive
109 2000307552 twobillionthreehundredseven|thousandfivehundredfiftytwo
110 2000700235 twobillionsevenhundredtho|usandtwohundredthirtyfive
111 2000700532 twobillionsevenhundredtho|usandfivehundredthirtytwo
112 2000703255 twobillionsevenhundredthree|thousandtwohundredfiftyfive
113 2000703552 twobillionsevenhundredthree|thousandfivehundredfiftytwo
114 2000710285 twobillionsevenhundredtent|housandtwohundredeightyfive
115 2000710582 twobillionsevenhundredtent|housandfivehundredeightytwo
116 2000732355 twobillionsevenhundredthirtyt|wothousandthreehundredfiftyfive
117 2000732553 twobillionsevenhundredthirtyt|wothousandfivehundredfiftythree
118 2000733255 twobillionsevenhundredthirtyt|hreethousandtwohundredfiftyfive
119 2000733552 twobillionsevenhundredthirtyt|hreethousandfivehundredfiftytwo
120 2000817255 twobillioneighthundredsevente|enthousandtwohundredfiftyfive
121 2000817552 twobillioneighthundredsevente|enthousandfivehundredfiftytwo
122 2000879285 twobillioneighthundredseventyn|inethousandtwohundredeightyfive
123 2000879582 twobillioneighthundredseventyn|inethousandfivehundredeightytwo
124 3000007055 threebillionseven|thousandfiftyfive
125 3000107155 threebilliononehundredseven|thousandonehundredfiftyfive
126 3000107551 threebilliononehundredseven|thousandfivehundredfiftyone
127 3000207255 threebilliontwohundredseven|thousandtwohundredfiftyfive
128 3000207552 threebilliontwohundredseven|thousandfivehundredfiftytwo
129 3000307355 threebillionthreehundredseven|thousandthreehundredfiftyfive
130 3000307553 threebillionthreehundredseven|thousandfivehundredfiftythree
131 3000407455 threebillionfourhundredseven|thousandfourhundredfiftyfive
132 3000407554 threebillionfourhundredseven|thousandfivehundredfiftyfour
133 3000507555 threebillionfivehundredseven|thousandfivehundredfiftyfive
134 3000607556 threebillionsixhundredseven|thousandfivehundredfiftysix
135 3000607655 threebillionsixhundredseven|thousandsixhundredfiftyfive
136 3000698434 threebillionsixhundredninetyeigh|tthousandfourhundredthirtyfour
...
10883 997000399055 ninehundredninetysevenbillionthree|hundredninetyninethousandfiftyfive
10884 998000063494 ninehundredninetyeightbillionsixty|threethousandfourhundredninetyfour
10885 998000064394 ninehundredninetyeightbillionsixty|fourthousandthreehundredninetyfour
10886 998000064493 ninehundredninetyeightbillionsixty|fourthousandfourhundredninetythree
10887 1000000611455 onetrillionsixhundredeleven|thousandfourhundredfiftyfive
10888 1000000611554 onetrillionsixhundredeleven|thousandfivehundredfiftyfour
10889 1000000700155 onetrillionsevenhundredt|housandonehundredfiftyfive
10890 1000000700551 onetrillionsevenhundredt|housandfivehundredfiftyone
The above spelled-out American integer names have the property that when the letters are replaced with their alphabetic rank (a=1, b=2, etc.), the product of the ranks to the left of the pipe is equal to the product of the ranks to the right of the pipe. Six of the integers (indicated by ==) allow an alternate split as the letter "a" is shifted from one side of the pipe to the other side (which has no effect on the products).
The idea is based on A372222 by Éric Angelini and Jean-Marc Falcoz wherein the ranks of the left/right parts of the split are summed instead of multiplied. I feel that this allows far too many solutions for the sequence to be interesting.
I have a full extended list of the above. The sequence is now in the OEIS. I have also added a large-number examples file evaluated at 10^3n up to 10^303.
No comments:
Post a Comment