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

Author

Amarnath Murthy, Nov 20 2002

Keywords

• base
• nonn

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.)

Examples

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

Links

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

Crossrefs

Cf. A002998, A069035.

Extensions

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

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