A385436 -id:A385436 - cp's OEIS frontend

A385455 First prepended column of the tribonacci array of the second kind, A385436.

-1, 0, 1, 2, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 68, 69, 70, 72, 73, 74, 75, 76, 77, 79, 80, 81

Offset: 1

A.H.M. Smeets, Jun 29 2025

sign

The numbers that do not occur in this sequence are given by A278041.

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

Cf. A278041, A385436.

A385532 Second prepended column of the tribonacci array of the second kind, A385436.

Original entry on oeis.org

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

Offset: 1

A.H.M. Smeets, Jul 02 2025

sign

The numbers that occur twice in this sequence are the numbers in A278039.

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

Cf. A278039, A385436.

A385533 Third prepended column of the tribonacci array of the second kind, A385436.

Original entry on oeis.org

-1, -1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 20, 21, 21, 21, 22, 22, 22, 23, 23, 24, 24, 24

Offset: 1

A.H.M. Smeets, Jul 02 2025

sign

The numbers that occur thrice in this sequence are given by A353084(n)-1, i.e., the first prepended column of the tribonacci array of the first kind minus one.

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

Cf. A353084, A385436.

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

Original entry on oeis.org

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

Tanya Khovanova and PRIMES STEP Senior group, May 04 2022

nonn

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

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

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

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

cp's OEIS Frontend

A385455 First prepended column of the tribonacci array of the second kind, A385436.

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A385532 Second prepended column of the tribonacci array of the second kind, A385436.

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A385533 Third prepended column of the tribonacci array of the second kind, A385436.

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

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Python