A336956 For any number n whose set of nonzero decimal digits is { d_0, ..., d_k } (with d_0 < ... < d_k), a(n) is obtained by replacing in the decimal representation of n each nonzero digit d_m by d_{k-m} for m = 0..k.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 21, 31, 41, 51, 61, 71, 81, 91, 20, 12, 22, 32, 42, 52, 62, 72, 82, 92, 30, 13, 23, 33, 43, 53, 63, 73, 83, 93, 40, 14, 24, 34, 44, 54, 64, 74, 84, 94, 50, 15, 25, 35, 45, 55, 65, 75, 85, 95, 60, 16, 26, 36, 46, 56, 66, 76

Offset: 0

Author

Rémy Sigrist, Aug 09 2020

Keywords

• nonn
• base

Comments

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

This sequence first differs from A321474 for n = 112: a(112) = 221 whereas A321474(112) = 211.

This sequence has similarities with A166166; here we consider nonzero decimal digits, there binary run-lengths.

Examples

			For n = 10251:
- the set of nonzero digits is { 1, 2, 5},
- so we replace each digit 1, 2, 5 respectively by 5, 2, 1,
- and a(10251) = 50215.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A125289, A166166, A321474.

Programs

PARI

a(n, base=10) = { my (d=digits(n, base), s=Set(select(sign, d))); fromdigits(apply (t -> if (t, s[#s+1-setsearch (s,t)], 0), d), base) }

Formula

a(n) = n iff n = 0 or n belongs to A125289.