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

0,3

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.

Links

Table of n, a(n) for n=0..54.

Rémy Sigrist, Perl program for A344486

Formula

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

Example

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.

Prog

(Perl) See Links section.

Crossrefs

Cf. A007953, A052018, A344487.

Sequence in context: A121760 A061816 A083960 * A138795 A297233 A382371

Adjacent sequences: A344483 A344484 A344485 * A344487 A344488 A344489

Keyword

nonn,base

Author

Rémy Sigrist, May 21 2021

Status

approved