A303002 - OEIS

%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