A319430 First differences of the tribonacci representation numbers (A003726 or A278038).

1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 10, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 5

Offset

0,7

Comments

This sequence appears to consist of runs of 1's of lengths given (essentially) by A275925, separated by single numbers > 1, which define the terms of A319431.

It would be nice to have a recurrence of some kind that produces A319431.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..50000 (first 9999 terms from N. J. A. Sloane)

Formula

Conjecture: All terms are of the form ceiling(2^k/7) for some k (cf. A046630), and all numbers of the form ceiling(2^k/7) occur.

Conjecture (continued): Furthermore, new values of ceiling(2^k/7) (that is, new records) appear at n = 0, 6,12, 23, 43, 80, 148, 273, ..., which (apart from the start) are the tribonacci numbers minus 1, A000073 - 1, or A089068.

a(n) = ceiling(2^i/7) iff the Tribonacci representation of n+1 ends in i 0's. - Jeffrey Shallit, Oct 02 2018

Mathematica

Differences@ Select[Range[0, 160], SequenceCount[IntegerDigits[#, 2], {1, 1, 1}] == 0 &] (* Michael De Vlieger, Dec 23 2019 *)

Crossrefs

Cf. A000073, A003726, A046630, A089068, A275925, A278038, A319431.

Sequence in context: A292435 A319094 A069283 * A285337 A328457 A340827

Adjacent sequences: A319427 A319428 A319429 * A319431 A319432 A319433

Keyword

nonn

Author

N. J. A. Sloane, Sep 30 2018

Status

approved