A344486 a(n) is the least k such that the sum of digits of k is a substring of n and the sum of digits of n is a substring of k.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 29, 39, 49, 59, 69, 79, 89, 99, 10, 2, 399, 499, 599, 699, 799, 899, 999, 101, 11, 3, 4999, 5999, 6999, 7999, 8999, 9999, 102, 111, 12, 4, 59999, 69999, 79999, 89999, 99999, 103, 112, 112, 13, 5, 699999, 799999, 899999, 999999

Offset: 0

Author

Rémy Sigrist, May 21 2021

Keywords

• nonn
• base

Comments

The sequence is well defined:

- for any number n with sum of digits d,

- by necessity, d <= n,

- the number k obtained by concatenating n-d 1's in front of d meets the requirements.

Examples

			For n = 11:
- the sum of digits of 11 is 2,
- the sum of digits of a(n) must equal 1 or 11,
    - the numbers whose sum of digits is 1 are the powers of 10,
    - 2 cannot be a substring of a power of 10,
    - the first number with sum of digits 11 is 29,
    - 2 is a substring of 29,
- so a(11) = 29.
		

Links

• Rémy Sigrist, Perl program for A344486

Crossrefs

Cf. A007953, A052018, A344487.

Programs

Perl

See Links section.

Formula

a(10 * n) = a(n).