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A342215
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Two successive terms always share a common "digit pattern" (see the Comments section). The successive "common digit patterns", concatenated, reproduce the successive terms of the sequence, concatenated.
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1
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1, 10, 100, 101, 1201, 301, 12, 20, 104, 13, 30, 102, 14, 21, 2, 200, 103, 410, 341, 3, 203, 105, 210, 421, 1242, 112, 204, 50, 106, 310, 34, 41, 107, 230, 43, 114, 31, 23, 205, 303, 113, 108, 305, 25, 121, 109, 40, 24, 123, 15, 120, 42, 1142, 211, 26, 207, 140, 45, 250, 110, 610, 36, 131, 160, 302, 134, 4
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OFFSET
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1,2
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COMMENTS
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A "common pattern" shared by two successive integers A and B is a string of digits present in both A and B. For example, if A = 1 and B = 10 the common pattern is "1"; if A = 2021 and B = 302 the common pattern is "02".
We allow the successive terms A and B to share more than one pattern, but only in the case of a single shared longer string of digits - longer than the other possible strings; as A = 2021 and B = 231 share both the strings "2" and "1", which are of the same length, B cannot follow A in the sequence. As A = 2021 and B = 2031 share both the strings "20" and "1" and as the string "20" is longer than the string "1", B could follow A in the sequence (the "common pattern" would be "20" here).
This "common pattern" idea was imagined to inspire people having almost no mathematical skills - only two eyes (or one single eye) and a pencil.
Caveat: to reduce the computing time, no term > 10000 was tested.
Given the doubts about this sequence, please do NOT add a b-file. N. J. A. Sloane, Mar 14 2021
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LINKS
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Table of n, a(n) for n=1..67.
Carole Dubois, Conjectured table of n, a(n) for n = 1..789
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EXAMPLE
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The first ten terms are 1, 10, 100, 101, 1201, 301, 12, 20, 104, 13.
The "common patterns" are 1 10 10 01 01 1 2 0 1 and their concatenation is 1101001011201 - which is exactly the start of the concatenation of the sequence's terms.
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CROSSREFS
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Cf. A152603
Sequence in context: A105424 A115832 A336611 * A342135 A169665 A257795
Adjacent sequences: A342212 A342213 A342214 * A342216 A342217 A342218
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KEYWORD
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base,nonn
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AUTHOR
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Eric Angelini and Carole Dubois, Mar 05 2021
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STATUS
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approved
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