

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
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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 nonrepunits 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

JeanMarc 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 JeanMarc Falcoz, Apr 17 2018


STATUS

approved



