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

1,1

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, ...

Links

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

Example

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

Prog

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

Crossrefs

Cf. A328447, A343852.

Sequence in context: A267761 A324322 A083826 * A331214 A364733 A270041

Adjacent sequences: A343885 A343886 A343887 * A343889 A343890 A343891

Keyword

nonn,look,base

Author

Ivan Neretin, May 02 2021

Status

approved