

A319430


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


2



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
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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



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



KEYWORD

nonn


AUTHOR



STATUS

approved



