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%I #23 Feb 28 2020 02:41:54
%S 1,2,3,4,5,6,7,8,9,11,26,16,28,12,18,34,29,13,14,21,19,111,31,27,37,
%T 1111,33,11111,111111,1111111,113,43,17,131,71,11111111,111111111,
%U 1111111111,11111111111,311,1113,111111111111,1111111111111,11111111111111,111111111111111,1111111111111111,11111111111111111,111111111111111111,1111111111111111111
%N Replacing each term of this sequence S with the product of its digits produces a new sequence S' such that S' and S share the same succession of digits.
%C The sequence starts with a(1) = 1 and is always extended with the smallest integer not yet present that doesn't lead to a contradiction.
%C Huge repunits appear quickly and leave almost no space for non-repunits in the sequence; a(112) = A002275(82), a(113) = 3111, a(114) = A002275(83) and nothing but repunits will show from there until at least a(303) = A002275(350).
%H Jean-Marc Falcoz, <a href="/A303002/b303002.txt">Table of n, a(n) for n = 1..302</a> (shortened by _N. J. A. Sloane_, Jan 18 2019)
%e The first nine terms are replaced by themselves;
%e 11 = a(10) is replaced by the product 1 * 1 = 1;
%e 26 = a(11) is replaced by the product 2 * 6 = 12;
%e 16 = a(12) is replaced by the product 1 * 6 = 6;
%e 28 = a(13) is replaced by the product 2 * 8 = 16;
%e 12 = a(14) is replaced by the product 1 * 2 = 2;
%e 18 = a(15) is replaced by the product 1 * 8 = 8;
%e 34 = a(16) is replaced by the product 3 * 4 = 12;
%e 29 = a(17) is replaced by the product 2 * 9 = 18;
%e 13 = a(18) is replaced by the product 1 * 3 = 3;
%e 14 = a(19) is replaced by the product 1 * 4 = 4;
%e etc.
%e We see that the first and the last column here (the terms of S and S') share the same succession of digits: 1,1,2,6,1,6,2,8,1,2,1,8,3,4,...
%Y Cf. A302656 where the word "product" is replaced by "sum".
%Y Cf. A002275 (repunits).
%K nonn,base
%O 1,2
%A _Eric Angelini_ and _Jean-Marc Falcoz_, Apr 17 2018
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