A379927 Replacing each term of this sequence S with its digitsum produces a new sequence S' such that S and S' share the same succession of nonzero digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 19, 18, 28, 17, 11, 26, 37, 16, 29, 20, 15, 12, 25, 46, 24, 101, 27, 110, 55, 14, 39, 200, 23, 13, 33, 299, 22, 38, 389, 34, 47, 32, 41, 59, 21, 36, 398, 479, 30, 49, 102, 111, 488, 45, 54, 497, 569, 120, 35, 201, 44, 63, 210, 31

Offset: 1

Author

Rémy Sigrist, Jan 06 2025

Keywords

• nonn
• base

Comments

The sequence starts with a(1) = 1 and is always extended with the smallest integer not yet present that doesn't lead to a contradiction.

This sequence is a variant of A302656 ignoring zeros; this feature prevents the huge jumps seen in A302656.

Examples

			The first terms are:
    1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 19, 18, 28, 17, 11, 26, 37, 16, 29, 20
The corresponding digitsums are:
    1, 2, 3, 4, 5, 6, 7, 8, 9, 1,  10, 9,  10, 8,  2,  8,  10, 7,  11, 2
Keeping only the nonzero digits we obtain:
    12345678911918281711263716292
and 123456789119182817112.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program

Crossrefs

Cf. A004719, A302656.

Programs

PARI

\\ See Links section.