A319967 a(n) = A003145(A003144(n)) where A003144 and A003145 are positions of '1' and '2' in the tribonacci word A092782.

2, 9, 15, 22, 26, 33, 39, 46, 53, 59, 66, 70, 77, 83, 90, 96, 103, 107, 114, 120, 127, 134, 140, 147, 151, 158, 164, 171, 175, 182, 188, 195, 202, 208, 215, 219, 226, 232, 239, 245, 252, 256, 263, 269, 276, 283, 289, 296, 300, 307, 313, 320, 327, 333, 340, 344

Offset: 1

Author

N. J. A. Sloane, Oct 05 2018

Keywords

• nonn
• easy

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 bac in the tribonacci word t = abacabaa..., fixed point of the morphism a->ab, b->ac, c->a. This follows from the fact that the word ac is always preceded in t by the letter b, and the formula BA = C-2, where A := A003144, B := A003145, C := A003146. - 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.

Crossrefs

Cf. A003144, A003145, A003146, A003622, A278039, A278040, A278041, and A319966-A319972.

Cf. A092782 (ternary tribonacci word).

Formula

a(n+1) = B(A(n)) = B(A(n) + 1) - 2 = A(n) + B(n) + n + 1, for n >= 0, where B = A278039 and A = A278040. For a proof see the W. Lang link in A278040, Proposition 9, eq. (51). - Wolfdieter Lang, Dec 13 2018

Extensions

More terms from Rémy Sigrist, Oct 16 2018