Exploring The Curiously Fascinating Integer Sequence 1,12,123,1234,12345,123456, 1234567,12345678,123456789, 1234567891,12345678912, 123456789123,. . .

JAY L. SCHIFFMAN

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Exploring The Curiously Fascinating Integer Sequence 1,12,123,1234,12345,123456, 1234567,12345678,123456789, 1234567891,12345678912, 123456789123,. . .

机译：探索令人着迷的整数序列1,12,123,1234,12345,123456，1234567,12345678,123456789，1234567891,12345678912，123456789123。。。

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This article considers the integer sequence 1, 12, 123, 1234, 12345, 123456, 1234567, 12345678, 123456789, 1234567891, 12345678912, 123456789123,....Our goal is to examine the structure of the sequence by exploring divisibility patterns including securing prime outputs and determining the highest power of two that is a possible factor of any term in the sequence. Using MATHEMATICA~?, I was able to obtain the complete prime factorizations for the initial 108 terms in the sequence. The deployment of modular arithmetic will enable us to secure recurring prime factors from complete groupings such as 123456789, 123456789123456789, 123456789123456789123456789, ....We conclude by suggesting future directions for companion sequences that serve to furnish additional stimulating research. Such possibilities include extensions, the sequence reversal, and examining the sequence and its reversals in different number bases such as hexadecimal and duodecimal (base twelve).

机译：本文考虑了整数序列1，12，123，1234，12345，123456，1234567，12345678，123456789，1234567891，12345678912，123456789123，....我们的目标是通过探索包括安全性在内的除数模式来检查序列的结构主输出并确定两个数的最高幂，这是序列中任何一项的可能因素。使用MATHEMATICA〜?，我能够获得序列中最初的108个项的完整素数分解。模块化算术的部署将使我们能够从完整的分组（例如123456789、123456789123456789、123456789123456789123456789等）中获得重复的主要因子，最后，我们建议了伴随序列的未来发展方向，以提供更多的刺激性研究。这样的可能性包括扩展，序列反转以及以不同的数字底数（例如十六进制和十二进制）（底数为十二）检查序列及其反转。

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《Mathematical spectrum》 |2016年第2期|共6页
作者
JAY L. SCHIFFMAN;
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正文语种 eng
中图分类数学;
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article; considers; integer;

机译：条款;考虑因素;整数;

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1. Exploring The Curiously Fascinating Integer Sequence 1,12,123,1234,12345,123456, 1234567,12345678,123456789, 1234567891,12345678912, 123456789123,. . . [J] . JAY L. SCHIFFMAN Mathematical spectrum . 2016,第2期

机译：探索令人着迷的整数序列1,12,123,1234,12345,123456，1234567,12345678,123456789，1234567891,12345678912，123456789123。。。
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4. On the average tractability of binary integer programming and the curious transition to perfect generalization in learning majority functions [C] . Shao C. Fang, Santosh S. Venkatesh Proceedings of the Sixth annual conference on Computational learning theory . 1993

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Exploring The Curiously Fascinating Integer Sequence 1,12,123,1234,12345,123456, 1234567,12345678,123456789, 1234567891,12345678912, 123456789123,. . .

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