A319966 - OEIS

%I #27 Jan 05 2025 19:51:41

%S 7,20,31,44,51,64,75,88,101,112,125,132,145,156,169,180,193,200,213,

%T 224,237,250,261,274,281,294,305,318,325,338,349,362,375,386,399,406,

%U 419,430,443,454,467,474,487,498,511,524,535,548,555,568,579,592,605,616

%N a(n) = A003144(A003146(n)).

%C By analogy with the Wythoff compound sequences A003622 etc., the nine compounds of A003144, A003145, A003146 might be called the tribonacci compound sequences. They are A278040, A278041, and A319966-A319972.

%C This sequence gives the positions of the word aa in the tribonacci word t = abacabaa..., fixed point of the morphism a->ab, b->ac, c->a.  This follows from the fact that the positional sequences of aa, ab and ac give a splitting of the positional sequence of the letter a, and the three sets AA(N), AB(N) and AC(N), give a splitting of the set A(N). Here A := A003144, B := A003145, C := A003146, and N is the set of positive integers. - _Michel Dekking_, Apr 09 2019

%H Rémy Sigrist, <a href="/A319966/b319966.txt">Table of n, a(n) for n = 1..10000</a>

%H Elena Barcucci, Luc Belanger and Srecko Brlek, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/42-4/quartbarcucci04_2004.pdf">On tribonacci sequences</a>, Fib. Q., 42 (2004), 314-320. Compare page 318.

%H L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/10-1/carlitz3-a.pdf">Fibonacci representations of higher order</a>, Fib. Quart., 10 (1972), 43-69, Theorem 13.

%H Rémy Sigrist, <a href="/A319966/a319966.pl.txt">Perl program for A319966</a>

%F a(n) = A319968(n) + 1. - _Michel Dekking_, Apr 04 2019

%o (Perl) See Links section.

%Y Cf. A003144, A003145, A003146, A003622, A278040, A278041, and A319966-A319972.

%K nonn,changed

%O 1,1

%A _N. J. A. Sloane_, Oct 05 2018

%E More terms from _Rémy Sigrist_, Oct 16 2018