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

1,1

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

Formula

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

Prog

(Perl) See Links section.

Crossrefs

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

Sequence in context: A134863 A214924 A333858 * A200773 A269044 A063235

Adjacent sequences: A319963 A319964 A319965 * A319967 A319968 A319969

Keyword

nonn

Author

N. J. A. Sloane, Oct 05 2018

Extensions

More terms from Rémy Sigrist, Oct 16 2018

Status

approved