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

0,3

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.

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

Formula

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

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

Example

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.

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 *)

Prog

(PARI) See Links section.

Crossrefs

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

Sequence in context: A390315 A069024 A175396 * A107085 A212499 A244890

Adjacent sequences: A338826 A338827 A338828 * A338830 A338831 A338832

Keyword

nonn,base

Author

Rémy Sigrist, Nov 11 2020

Status

approved