A343888 Smallest positive integer such that the decimal representations of a(n) and of a(n)+9n (both without leading zeros) are permutations of each other.

12, 13, 14, 15, 16, 17, 18, 19, 109, 120, 102, 102, 124, 125, 126, 127, 128, 129, 130, 130, 123, 103, 103, 135, 136, 137, 138, 139, 140, 140, 134, 124, 104, 104, 146, 147, 148, 149, 150, 150, 145, 135, 125, 105, 105, 157, 158, 159, 160, 160, 156, 146, 136, 126, 106, 106, 168, 169, 170, 170

Offset: 1

Author

Ivan Neretin, May 02 2021

Keywords

• nonn
• look
• base

Comments

A concatenation of 10 and n provides the proof of existence and also an upper bound for a(n).

The bound is exact for n = 9, 90, 900, ...

Examples

			102 + 9*11 = 201 which is a permutation of digits of 102, and no smaller number has this feature, hence a(11)=102.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..8999

Crossrefs

Cf. A328447, A343852.

Programs

PARI

a(n) = { for (v=1, oo, if (vecsort(digits(v))==vecsort(digits(v+9*n)), return (v))) } \\ Rémy Sigrist, May 03 2021