A289410 -id:A289410 - cp's OEIS frontend

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

Rémy Sigrist, Nov 11 2020

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.

			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.

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

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

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
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See Links section.
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A055642(a(n)) = A055642(n).

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

A332144 Nonnegative numbers ordered by number of digits, and then by sum of digits, and then by value.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 12, 21, 30, 13, 22, 31, 40, 14, 23, 32, 41, 50, 15, 24, 33, 42, 51, 60, 16, 25, 34, 43, 52, 61, 70, 17, 26, 35, 44, 53, 62, 71, 80, 18, 27, 36, 45, 54, 63, 72, 81, 90, 19, 28, 37, 46, 55, 64, 73, 82, 91, 29, 38, 47, 56

Offset: 0

Rémy Sigrist, Nov 20 2020

This sequence is a permutation of the nonnegative integers with inverse A332166.

This sequence can also be seen as an irregular triangle with first row consisting of a zero, and subsequent row lengths given by A289410.

			Triangle starts:
    0;
    1;
    2;
    3;
    4;
    5;
    6;
    7;
    8;
    9;
    10;
    11, 20;
    12, 21, 30;
    13, 22, 31, 40;
    14, 23, 32, 41, 50;
    15, 24, 33, 42, 51, 60;
    16, 25, 34, 43, 52, 61, 70;
    17, 26, 35, 44, 53, 62, 71, 80;
    18, 27, 36, 45, 54, 63, 72, 81, 90;
    19, 28, 37, 46, 55, 64, 73, 82, 91;
    29, 38, 47, 56, 65, 74, 83, 92;
    39, 48, 57, 66, 75, 84, 93;
    49, 58, 67, 76, 85, 94;
    59, 68, 77, 86, 95;
    69, 78, 87, 96;
    79, 88, 97;
    89, 98;
    99;
    ...

Rémy Sigrist, Table of n, a(n) for n = 0..9999
Rémy Sigrist, PARI program for A332144
Index entries for sequences that are permutations of the natural numbers

Cf. A187769 (binary analog), A289410, A332166 (inverse).

PARI
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See Links section.
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a(10^k - 1) = 10^k - 1 for any k >= 0.
a(10^k) = 10^k for any k >= 0.
a(10^k + 1) = 10^k + 1 for any k >= 0.

cp's OEIS Frontend

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.

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