A075154 a(n) is the smallest multiple of n such that a(n) mod 100 = n and S(n)=n where S(n) is the sum of the base-ten digits of n, or 0 if no such a(n) exists.

1, 2, 3, 4, 5, 6, 7, 8, 9, 910, 0, 912, 11713, 6314, 915, 3616, 15317, 918, 17119, 9920, 18921, 9922, 82823, 19824, 9925, 46826, 18927, 18928, 78329, 99930, 585931, 388832, 1098933, 198934, 289835, 99936, 99937, 478838, 198939, 1999840

Offset: 1

Author

Sandro Boscaro (sboscaro(AT)libero.it), Sep 06 2002

Keywords

• nonn
• base
• fini
• full

Comments

The modulo requirements means values up to n=99 can be computed. - R. J. Mathar, Feb 08 2023

Examples

			a(10)=910 since 10 divides 910, 9 + 1 + 0 = 10 and 910 ends with 10.
		

References

• Sandro Boscaro, Nivenmorphic Integers, Journal of Recreational Mathematics, Vol. 28 (1996-97), Number 3, pp. 201-205.

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..99
• Index entries for sequences related to automorphic numbers

Crossrefs

Cf. A005349, A187924.

Extensions

Edited by Matthew Conroy, Oct 21 2002