

A342215


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.


1



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

1,2


COMMENTS

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 bfile. N. J. A. Sloane, Mar 14 2021


LINKS

Table of n, a(n) for n=1..67.
Carole Dubois, Conjectured table of n, a(n) for n = 1..789


EXAMPLE

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.


CROSSREFS

Cf. A152603
Sequence in context: A105424 A115832 A336611 * A342135 A169665 A257795
Adjacent sequences: A342212 A342213 A342214 * A342216 A342217 A342218


KEYWORD

base,nonn


AUTHOR

Eric Angelini and Carole Dubois, Mar 05 2021


STATUS

approved



