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, 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

Offset: 1

Author

Eric Angelini and Carole Dubois, Mar 05 2021

Keywords

• base
• nonn

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 b-file. N. J. A. Sloane, Mar 14 2021

Examples

			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.
		

Links

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

Crossrefs

Cf. A152603