A338829 - OEIS

%I #19 Nov 14 2020 01:50:11

%S 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,

%T 71,81,82,92,12,22,32,42,52,62,72,73,83,93,13,23,33,43,53,63,64,74,84,

%U 94,14,24,34,44,54,55,65,75,85,95,15,25,35,45,46,56,66,76

%N 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.

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

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

%H Rémy Sigrist, <a href="/A338829/b338829.txt">Table of n, a(n) for n = 0..9999</a>

%H Rémy Sigrist, <a href="/A338829/a338829.png">Colored scatterplot of the first 10000 terms</a> (where the color is function of the sum of digits of n)

%H Rémy Sigrist, <a href="/A338829/a338829.gp.txt">PARI program for A338829</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F A055642(a(n)) = A055642(n).

%F A007953(a(n)) = A007953(n).

%e For n = 23:

%e - the numbers with 2 digits and sum of digits 5 are: 14, 23, 32, 41 and 50,

%e - so  a(14) = 50,

%e       a(23) = 41,

%e       a(32) = 32,

%e       a(41) = 23,

%e       a(50) = 14.

%t 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 *)

%o (PARI) See Links section.

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

%K nonn,base

%O 0,3

%A _Rémy Sigrist_, Nov 11 2020