A342115 Lexicographically latest sequence of distinct nonnegative integers such that the multisets of frequencies of digits in the decimal representations of n and of a(n) are the same.

0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 98, 99, 97, 96, 95, 94, 93, 92, 91, 90, 89, 87, 88, 86, 85, 84, 83, 82, 81, 80, 79, 78, 76, 77, 75, 74, 73, 72, 71, 70, 69, 68, 67, 65, 66, 64, 63, 62, 61, 60, 59, 58, 57, 56, 54, 55, 53, 52, 51, 50, 49, 48, 47, 46, 45, 43, 44, 42

Offset

0,2

Comments

We ignore leading zeros (hence a(0) = 0).

This sequence is a self-inverse permutation of the nonnegative integers.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..9999

Rémy Sigrist, PARI program for A342115

Index entries for sequences that are permutations of the natural numbers

Formula

a(d * (10^k-1)/9) = (10-d) * (10^k-1)/9 for any k >= 0 and d = 1..9.

a(n) < 10^k for any n < 10^k.

Example

Consider the set of numbers T with two distinct digits, say u and v, such that u appears once and v appears twice:
- the least elements of T are: 100, 101, 110, 112,
- the greatest elements of T are: 995, 996, 997, 998,
- so a(100) = 998, a(101) = 997, a(110) = 996, a(112) = 995.

Prog

(PARI) See Links section.

Crossrefs

See A342102 for similar sequences.

Cf. A055641, A268643, A316863, A316864, A316865, A316866, A316867, A316868, A316869, A102683.

Sequence in context: A298372 A089186 A055120 * A090671 A132673 A363249

Adjacent sequences: A342112 A342113 A342114 * A342116 A342117 A342118

Keyword

nonn,base

Author

Rémy Sigrist, Feb 28 2021

Status

approved