A319966 a(n) = A003144(A003146(n)).

7, 20, 31, 44, 51, 64, 75, 88, 101, 112, 125, 132, 145, 156, 169, 180, 193, 200, 213, 224, 237, 250, 261, 274, 281, 294, 305, 318, 325, 338, 349, 362, 375, 386, 399, 406, 419, 430, 443, 454, 467, 474, 487, 498, 511, 524, 535, 548, 555, 568, 579, 592, 605, 616

Offset: 1

Author

N. J. A. Sloane, Oct 05 2018

Keywords

• nonn

Comments

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.

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

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Elena Barcucci, Luc Belanger and Srecko Brlek, On tribonacci sequences, Fib. Q., 42 (2004), 314-320. Compare page 318.
• L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., Fibonacci representations of higher order, Fib. Quart., 10 (1972), 43-69, Theorem 13.
• Rémy Sigrist, Perl program for A319966

Crossrefs

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

Programs

Perl

See Links section.

Formula

a(n) = A319968(n) + 1. - Michel Dekking, Apr 04 2019

Extensions

More terms from Rémy Sigrist, Oct 16 2018