A263019 If n is the i-th positive integer with digital sum j, then a(n) is the j-th positive integer with digital sum i.

1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 2, 11, 20, 101, 110, 200, 1001, 1010, 1100, 1000000000, 12, 21, 30, 102, 111, 120, 201, 210, 2000, 10000000000, 22, 31, 40, 103, 112, 121, 130, 300, 10001, 100000000000, 32, 41, 50, 104, 113, 122

Offset: 1

Author

Paul Tek, Oct 07 2015

Keywords

• nonn
• base

Comments

Digital sum is given by A007953.

This is a self-inverse permutation of the natural numbers, with fixed points A081927.

A007953(n) = A081927(a(n)) for any n>0.

A081927(n) = A007953(a(n)) for any n>0.

a(A051885(n)) = 10^(n-1) for any n>0.

a(10^(n-1)) = A051885(n) for any n>0.

Links

• Paul Tek, Table of n, a(n) for n = 1..10000
• Paul Tek, PERL program for this sequence

Crossrefs

Cf. A007953, A051885, A081927, A254524, A263018.

Programs

PARI

a(n) = {j = sumdigits(n); v = vector(n, k, sumdigits(k)); i = #select(x->x==j, v); nb = 0; k = 0; while(nb != j, k++; if (sumdigits(k) == i, nb++)); k;} \\ Michel Marcus, Oct 16 2015