A321474 Reverse the nonzero digits of n.

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, Nov 11 2018

Keywords

• nonn
• base

Comments

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

See A321464 for the ternary variant.

This sequence has similarities with A069799: here we reverse nonzero digits, there we reverse nonzero prime exponents.

Examples

			For n = 1024:
- 1024 has 3 nonzero digits: 1, 2 and 4,
- so we replace the first nonzero digit by the third, the third by the first (and the second remains in place),
- and we obtain a(1024) = 4021.
		

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. A004086, A069799, A136400, A321464.

Programs

PARI

a(n, base=10) = my (d=digits(n, base), t=Vecrev(select(sign, d)), i=0); for (j=1, #d, if (d[j], d[j] = t[i++])); fromdigits(d, base)

Formula

a(10 * n) = 10 * a(n).

A136400(a(n)) = A136400(n).