A338831 a(n) is the greatest number not yet in the sequence with the same number of digits and the same smallest digit as n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 90, 91, 81, 71, 61, 51, 41, 31, 21, 19, 80, 18, 92, 82, 72, 62, 52, 42, 32, 29, 70, 17, 28, 93, 83, 73, 63, 53, 43, 39, 60, 16, 27, 38, 94, 84, 74, 64, 54, 49, 50, 15, 26, 37, 48, 95, 85, 75, 65, 59, 40, 14, 25, 36, 47, 58, 96, 86

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 smallest digit of n)

Rémy Sigrist, PARI program for A338831

Index entries for sequences that are permutations of the natural numbers

Formula

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

A054054(a(n)) = A054054(n).

Example

For n = 77:
- the numbers with 2 digits and smallest digit 7 are: 77, 78, 79, 87 and 97,
- so a(77) = 97,
     a(78) = 87,
     a(79) = 79,
     a(87) = 78,
     a(97) = 77.

Mathematica

Block[{a = {}, f, k}, f[x_] := Min@ 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. A054054, A055642, A338830.

Sequence in context: A273478 A278944 A303171 * A024664 A078188 A240511

Adjacent sequences: A338828 A338829 A338830 * A338832 A338833 A338834

Keyword

nonn,base

Author

Rémy Sigrist, Nov 11 2020

Status

approved