A338829 a(n) is the greatest number not yet in the sequence with the same number of digits and the same sum of digits as n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 91, 11, 21, 31, 41, 51, 61, 71, 81, 82, 92, 12, 22, 32, 42, 52, 62, 72, 73, 83, 93, 13, 23, 33, 43, 53, 63, 64, 74, 84, 94, 14, 24, 34, 44, 54, 55, 65, 75, 85, 95, 15, 25, 35, 45, 46, 56, 66, 76

Offset: 0

Author

Rémy Sigrist, Nov 11 2020

Keywords

• nonn
• base

Comments

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

We have a fixed point with m digits and sum of digits k whenever A289410(m, k) is odd.

Examples

			For n = 23:
- the numbers with 2 digits and sum of digits 5 are: 14, 23, 32, 41 and 50,
- so  a(14) = 50,
      a(23) = 41,
      a(32) = 32,
      a(41) = 23,
      a(50) = 14.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..9999
• Rémy Sigrist, Colored scatterplot of the first 10000 terms (where the color is function of the sum of digits of n)
• Rémy Sigrist, PARI program for A338829
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A055642, A289410, A331274 (binary analog), A333659, A338834 (factorial base analog), A338835 (primorial base analog).

Programs

Mathematica

Block[{a = {}, f, k}, f[x_] := Total@ IntegerDigits@ x; Do[k = f[i]; AppendTo[a, SelectFirst[Range[10^# - 1, 10^(# - 1), -1] &@ Floor[1 + Log10[i]], And[f[#] == k, FreeQ[a, #]] &]], {i, 67}]; a] (* Michael De Vlieger, Nov 13 2020 *)

PARI

See Links section.

Formula

A055642(a(n)) = A055642(n).

A007953(a(n)) = A007953(n).