OFFSET

0,2

COMMENTS

This sequence gives the A(n) numbers of the W. Lang link. There the B(n) and C(n) numbers are A278039(n) and A278041(n), respectively. - Wolfdieter Lang, Dec 05 2018

Positions of letter b in the tribonacci word t generated by a->ab, b->ac, c->a, when given offset 0. - Michel Dekking, Apr 03 2019

This sequence gives the positions of the word ab in the tribonacci word t. This follows from the fact that the letter b is always preceded in t by the letter a, and the formula AA = B-1, where A := A003144, B := A003145, C := A003146. - Michel Dekking, Apr 09 2019

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 0..20000

L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., Fibonacci representations of higher order, Fib. Quart., 10 (1972), 43-69.

Wolfdieter Lang, The Tribonacci and ABC Representations of Numbers are Equivalent, arXiv:1810.09787v1 [math.NT], 2018.

FORMULA

a(n) = A003145(n+1) - 1.

See Theorem 13 in the Carlitz, Scoville and Hoggatt paper. - Michel Dekking, Mar 20 2019

From Wolfdieter Lang, Dec 13 2018: (Start)

This sequence gives the indices k with A080843(k) = 1, ordered increasingly with offset 0.

For a proof see the W. Lang link, Proposition 5, and eq. (58).

a(n) - 1 = B1(n), where B1-numbers are B-numbers from A278039 followed by an A-number from A278040. See a comment and example in A319968.

a(n) - 1 = B(B(n)) = B(B(n) + 1) - 2, for n > = 0, where B = A278039.

(End)

EXAMPLE

The tribonacci representation of 7 is 1000 (see A278038), so a(7) has tribonacci representation 100001, which is 24+1 = 25, so a(7) = 25.

CROSSREFS

KEYWORD

nonn,base,easy

AUTHOR

N. J. A. Sloane, Nov 18 2016

STATUS

approved