A353086 Column -1 of the extended Trithoff (Tribonacci) array.

0, 1, 1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 8, 9, 10, 10, 11, 12, 12, 13, 14, 14, 15, 16, 16, 17, 18, 18, 19, 20, 20, 21, 21, 22, 23, 23, 24, 25, 25, 26, 27, 27, 28, 29, 29, 30, 31, 31, 32, 32, 33, 34, 34, 35, 36, 36, 37, 38, 38, 39, 40, 40, 41, 42, 42, 43, 44, 44, 45, 45, 46, 47, 47, 48, 49, 49, 50

Offset: 1

Author

Tanya Khovanova and PRIMES STEP Senior group, Apr 22 2022

Keywords

• nonn

Comments

This column is also called the seed of the Trithoff array.

This is a nondecreasing sequence containing all nonnegative integers, with some of them doubled. The doubled numbers are the positions of the letter "a" in the Tribonacci word (A003144). Correspondingly, single numbers are positions of letters "b" and "c" in the Tribonacci word.

Suppose number n_1 has Tribonacci representation t that ends in 1 (such numbers are in column 1 of the Trithoff array). Then its Tribonacci successor n_2 has Tribonacci representation t0 (such numbers are in column 2 of the Trithoff array), and the successor of the successor n_3 has Tribonacci representation t00 (such numbers are in column 3 of the Trithoff array). The seed in the same row as n_1, n_2, and n_3 is 2n_2-n_3.

Crossrefs

Cf. A000073, A003144, A003145, A003146, A136175, A353083, A353084, A353090.