A077754 Smallest multiple of n with two or more digits, none of them zeros, whose digit sum equals n, or 0 if no such multiple exists.

0, 0, 12, 112, 0, 24, 133, 152, 18, 0, 0, 48, 247, 266, 195, 448, 476, 198, 874, 0, 399, 2398, 1679, 888, 4975, 1898, 999, 7588, 4988, 0, 8959, 17888, 42999, 28798, 57995, 29988, 37999, 59888, 49998, 0, 177899, 88998, 99889, 479996, 499995, 589996

Offset

1,3

Comments

Equivalently, the digits of a(n) are a nontrivial composition of n and n divides a(n).

Conjecture: zero occurs only for indices which are multiples of 10 apart from 1, 2, 5 and 11. (a(n) = 0 only for n = 1,2,5,11 or n = 10k.)

Links

Chai Wah Wu, Table of n, a(n) for n = 1..100

Example

a(8) = 152 is a multiple of 8; a(10) = 0, since every multiple of 10 includes a 0.

Crossrefs

Cf. A002998, A069035.

Sequence in context: A123933 A199691 A348150 * A199357 A293872 A044344

Adjacent sequences: A077751 A077752 A077753 * A077755 A077756 A077757

Keyword

base,nonn

Author

Amarnath Murthy, Nov 20 2002

Extensions

Edited and extended by Franklin T. Adams-Watters, Jun 14 2006

a(44) corrected by Chai Wah Wu, Mar 17 2016

Status

approved