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

1,2

Comments

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

References

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

Links

Table of n, a(n) for n=1..40.

Index entries for sequences related to automorphic numbers

Example

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

Crossrefs

Cf. A005349, A187924.

Sequence in context: A257275 A112014 A145461 * A187924 A352462 A070938

Adjacent sequences: A075151 A075152 A075153 * A075155 A075156 A075157

Keyword

nonn,base,fini

Author

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

Extensions

Edited by Matthew Conroy, Oct 21 2002

Status

approved