A319434 Take Golomb's sequence A001462 and shorten all the runs by 1.

2, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19

Offset: 1

Author

N. J. A. Sloane, Oct 02 2018

Keywords

• nonn

Comments

In other words, apply Lenormand's "raboter" transformation (see A318921) to A001462.

Each value of n (n >= 2) appears exactly A001462(n)-1 times.

There should be a simple formula for a(n), just as there is for Golomb's sequence. - N. J. A. Sloane, Nov 15 2018. After 10000 terms, a(n) seems to be growing like constant*n^0.640. - N. J. A. Sloane, Jun 04 2021

Examples

			Golomb's sequence begins 1, 2,2, 3,3, 4,4,4, 5,5,5, ...
and we just shorten each run by one term, getting 2, 3, 4,4, 5,5, ...
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Brady Haran and N. J. A. Sloane, Planing Sequences (Le Rabot), Numberphile video, June 2021.
• N. J. A. Sloane, Coordination Sequences, Planing Numbers, and Other Recent Sequences (II), Experimental Mathematics Seminar, Rutgers University, Jan 31 2019, Part I, Part 2, Slides. (Mentions this sequence)

Crossrefs

Cf. A001462, A318921, A319951.

Formula

a(n) = A001462(A001462(A001462(n) + n) + n). - Alan Michael Gómez Calderón, Aug 14 2025

Extensions

More terms from Rémy Sigrist, Oct 04 2018