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.

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, 1111, 33, 11111, 111111, 1111111, 113, 43, 17, 131, 71, 11111111, 111111111, 1111111111, 11111111111, 311, 1113, 111111111111, 1111111111111, 11111111111111, 111111111111111, 1111111111111111, 11111111111111111, 111111111111111111, 1111111111111111111

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Apr 17 2018

Keywords

• nonn
• base

Comments

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.

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).

Examples

			The first nine terms are replaced by themselves;
11 = a(10) is replaced by the product 1 * 1 =  1;
26 = a(11) is replaced by the product 2 * 6 = 12;
16 = a(12) is replaced by the product 1 * 6 =  6;
28 = a(13) is replaced by the product 2 * 8 = 16;
12 = a(14) is replaced by the product 1 * 2 =  2;
18 = a(15) is replaced by the product 1 * 8 =  8;
34 = a(16) is replaced by the product 3 * 4 = 12;
29 = a(17) is replaced by the product 2 * 9 = 18;
13 = a(18) is replaced by the product 1 * 3 =  3;
14 = a(19) is replaced by the product 1 * 4 =  4;
etc.
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,...
		

Links

• Jean-Marc Falcoz, Table of n, a(n) for n = 1..302 (shortened by _N. J. A. Sloane_, Jan 18 2019)

Crossrefs

Cf. A302656 where the word "product" is replaced by "sum".

Cf. A002275 (repunits).