cp's OEIS Frontend

A303002 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.

%I A303002 #23 Feb 28 2020 02:41:54
%S A303002 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 A303002 1111,33,11111,111111,1111111,113,43,17,131,71,11111111,111111111,
%U A303002 1111111111,11111111111,311,1113,111111111111,1111111111111,11111111111111,111111111111111,1111111111111111,11111111111111111,111111111111111111,1111111111111111111
%N A303002 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 A303002 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 A303002 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 A303002 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 A303002 The first nine terms are replaced by themselves;
%e A303002 11 = a(10) is replaced by the product 1 * 1 =  1;
%e A303002 26 = a(11) is replaced by the product 2 * 6 = 12;
%e A303002 16 = a(12) is replaced by the product 1 * 6 =  6;
%e A303002 28 = a(13) is replaced by the product 2 * 8 = 16;
%e A303002 12 = a(14) is replaced by the product 1 * 2 =  2;
%e A303002 18 = a(15) is replaced by the product 1 * 8 =  8;
%e A303002 34 = a(16) is replaced by the product 3 * 4 = 12;
%e A303002 29 = a(17) is replaced by the product 2 * 9 = 18;
%e A303002 13 = a(18) is replaced by the product 1 * 3 =  3;
%e A303002 14 = a(19) is replaced by the product 1 * 4 =  4;
%e A303002 etc.
%e A303002 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 A303002 Cf. A302656 where the word "product" is replaced by "sum".
%Y A303002 Cf. A002275 (repunits).
%K A303002 nonn,base
%O A303002 1,2
%A A303002 _Eric Angelini_ and _Jean-Marc Falcoz_, Apr 17 2018