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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
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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).

LINKS

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

EXAMPLE

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,...

CROSSREFS

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

Cf. A002275 (repunits).

Sequence in context: A250411 A250410 A250409 * A167152 A246008 A064704

Adjacent sequences:  A302999 A303000 A303001 * A303003 A303004 A303005

KEYWORD

nonn,base

AUTHOR

Eric Angelini and Jean-Marc Falcoz, Apr 17 2018

STATUS

approved

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Last modified August 3 13:49 EDT 2020. Contains 336198 sequences. (Running on oeis4.)