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a(n) = A140099(n) - A140101(n).
17

%I #40 Mar 19 2019 13:02:24

%S 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,

%T 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,

%U 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

%N a(n) = A140099(n) - A140101(n).

%C 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.)

%C 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

%C 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

%H N. J. A. Sloane, <a href="/A275926/b275926.txt">Table of n, a(n) for n = 1..50000</a> [Corrected Mar 16 2019. The old b-file had errors]

%H L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., <a href="http://www.fq.math.ca/Scanned/10-1/carlitz3-a.pdf">Fibonacci representations of higher order</a>, Fib. Quart., 10 (1972), 43-69.

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

%K sign

%O 1

%A _N. J. A. Sloane_, Aug 29 2016