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

1,2

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

Prog

(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

Crossrefs

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

Sequence in context: A191231 A326494 A285593 * A248898 A207188 A085148

Adjacent sequences: A351628 A351629 A351630 * A351632 A351633 A351634

Keyword

nonn

Author

Tanya Khovanova and PRIMES STEP Senior group, May 04 2022

Status

approved