%I
%S 1,10,100,101,1201,301,12,20,104,13,30,102,14,21,2,200,103,410,341,3,
%T 203,105,210,421,1242,112,204,50,106,310,34,41,107,230,43,114,31,23,
%U 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
%N 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.
%C 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".
%C 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).
%C This "common pattern" idea was imagined to inspire people having almost no mathematical skills  only two eyes (or one single eye) and a pencil.
%C Caveat: to reduce the computing time, no term > 10000 was tested.
%C Given the doubts about this sequence, please do NOT add a bfile. _N. J. A. Sloane_, Mar 14 2021
%H Carole Dubois, <a href="/A342215/a342215.txt">Conjectured table of n, a(n) for n = 1..789</a>
%e The first ten terms are 1, 10, 100, 101, 1201, 301, 12, 20, 104, 13.
%e 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.
%Y Cf. A152603
%K base,nonn
%O 1,2
%A _Eric Angelini_ and _Carole Dubois_, Mar 05 2021
