A338830 a(n) is the greatest number not yet in the sequence with the same number of digits and the same largest digit as n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 10, 22, 33, 44, 55, 66, 77, 88, 99, 21, 20, 12, 32, 43, 54, 65, 76, 87, 98, 31, 30, 23, 13, 42, 53, 64, 75, 86, 97, 41, 40, 34, 24, 14, 52, 63, 74, 85, 96, 51, 50, 45, 35, 25, 15, 62, 73, 84, 95, 61, 60, 56, 46, 36, 26, 16, 72

Offset

0,3

Comments

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

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 largest digit of n)

Rémy Sigrist, PARI program for A338830

Index entries for sequences that are permutations of the natural numbers

Formula

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

A054055(a(n)) = A054055(n).

Example

For n = 20:
- the numbers with 2 digits and largest digit 2 are: 12, 20, 21 and 22,
- so a(12) = 22,
     a(20) = 21,
     a(21) = 20,
     a(22) = 12.

Mathematica

Block[{a = {}, f, k}, f[x_] := Max@ 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. A054055, A055642, A338831.

Sequence in context: A065650 A358386 A065649 * A262037 A262039 A354719

Adjacent sequences: A338827 A338828 A338829 * A338831 A338832 A338833

Keyword

nonn,base

Author

Rémy Sigrist, Nov 11 2020

Status

approved