A275926 a(n) = A140099(n) - A140101(n).

0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1

Offset

1

Comments

Conjecture: a(n) = floor(n*t) - A003144(n), where t is the tribonacci constant A058265. - N. J. A. Sloane, Oct 28 2016 (Changed from an assertion to a conjecture by N. J. A. Sloane, Mar 19 2019.)

Theorem: floor(n*t) - A003144(n) is always in {-1, 0, 1}, but the first place where it equals -1 is n = 12737. - Jeffrey Shallit, Nov 19 2016

It follows from Theorem 18 in the Carlitz, Scoville and Hoggatt paper that the values -1, 0 and 1 are taken infinitely often. - Michel Dekking, Mar 19 2019

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..50000 [Corrected Mar 16 2019. The old b-file had errors]

L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., Fibonacci representations of higher order, Fib. Quart., 10 (1972), 43-69.

Crossrefs

Cf. A140099, A140101, A275927 (run lengths), A276407 (positions of 1's), A003144, A058265, A275158 (positions of -1's).

Sequence in context: A059437 A152592 A347412 * A131533 A131532 A353513

Adjacent sequences: A275923 A275924 A275925 * A275927 A275928 A275929

Keyword

sign

Author

N. J. A. Sloane, Aug 29 2016

Status

approved