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

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

Author

Rémy Sigrist, Nov 20 2020

Keywords

• nonn
• base
• tabf

Comments

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.

Examples

			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;
    ...
		

Links

• 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

Crossrefs

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

Programs

PARI

See Links section.

Formula

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.