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

1,1

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

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)

Example

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, ...

Crossrefs

Cf. A001462, A318921, A319951.

Sequence in context: A327704 A360924 A027434 * A174697 A176504 A196162

Adjacent sequences: A319431 A319432 A319433 * A319435 A319436 A319437

Keyword

nonn

Author

N. J. A. Sloane, Oct 02 2018

Extensions

More terms from Rémy Sigrist, Oct 04 2018

Status

approved