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

Author

Rémy Sigrist, Feb 28 2021

Keywords

• nonn
• base

Comments

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

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

Examples

			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.
		

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

Crossrefs

See A342102 for similar sequences.

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

Programs

PARI

See Links section.

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.