A351631 The numbers that are not doubled in column -1 of the extended Trithoff (tribonacci) array.

0, 2, 4, 6, 9, 11, 13, 15, 17, 19, 22, 24, 26, 28, 30, 33, 35, 37, 39, 41, 43, 46, 48, 50, 53, 55, 57, 59, 61, 63, 66, 68, 70, 72, 74, 77, 79, 81, 83, 85, 87, 90, 92, 94, 96, 98, 100, 103, 105, 107, 109, 111, 114, 116, 118, 120, 122, 124, 127, 129, 131, 134, 136, 138, 140, 142, 144, 147, 149, 151

Offset: 1

Author

Tanya Khovanova and PRIMES STEP Senior group, May 04 2022

Keywords

• nonn

Comments

Excluding zeros, these are the indices of letters b and c in the tribonacci word.

The complement of A003144: the indices of the letter a in the tribonacci word. These numbers are doubled in column -1 in the extended Trithoff array.

Also integers with "even" lazy tribonacci representation A352103, and first column of A385436. - A.H.M. Smeets, Jun 29 2025

Links

• A.H.M. Smeets, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000073, A003144, A003145, A003146, A136175, A353083, A353084, A353086, A353090.

Programs

Python

def ToDual_111_Zeck(n):
    if n == 0:
        return "0"
    f0, f1, f2, sf = 1, 0, 0, 0
    while n > sf:
        f0, f1, f2 = f0+f1+f2, f0, f1
        sf += f0
    r, s = sf-n, "1"
    while f0 > 1:
        f0, f1, f2 = f1, f2, f0-f1-f2
        r, s = r%f0, s+str(1-r//f0)
    return s
n, a = 0, 0
while n < 70:
    s = ToDual_111_Zeck(a)
    if s[len(s)-1] == "0": # == even
        n += 1
        print(a, end = ", ")
a += 1 # A.H.M. Smeets, Jun 28 2025