A356899 -id:A356899 - cp's OEIS frontend

A356965 a(n) is the sum of the tribonacci numbers in common in the greedy and lazy tribonacci representations of n.

0, 1, 2, 3, 4, 5, 6, 0, 8, 9, 10, 11, 12, 0, 1, 15, 16, 17, 18, 19, 13, 21, 22, 23, 0, 1, 2, 3, 28, 29, 30, 24, 32, 33, 34, 35, 36, 24, 25, 39, 40, 41, 42, 43, 0, 1, 2, 3, 4, 5, 6, 7, 52, 53, 54, 55, 56, 44, 45, 59, 60, 61, 62, 63, 57, 65, 66, 67, 44, 45, 46

Offset: 0

Rémy Sigrist, Sep 06 2022

This sequence is to tribonacci numbers (A000073) what A356771 is to Fibonacci numbers (A000045).

			For n = 58:
- with T = A000073,
- the greedy representation of 58 is: T(9) + T(7) + T(3),
- the lazy representation of 58 is: T(9) + T(6) + T(5) + T(4) + T(3),
- so a(59) = T(9) + T(3) = 45.

Rémy Sigrist, Table of n, a(n) for n = 0..10609
Rémy Sigrist, PARI program
Index entries for sequences related to Zeckendorf expansion of n

Cf. A000045, A000073, A003726, A003796, A356771, A356899, A356964, A356966.

PARI
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See Links section.
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a(n) = A356964(A003796(n+1) AND A003726(n+1)) (where AND denotes the bitwise AND operator).
a(n) <= n with equality iff n belongs to A356899.
a(n) = 0 iff n belongs to A356966.

cp's OEIS Frontend

A356965 a(n) is the sum of the tribonacci numbers in common in the greedy and lazy tribonacci representations of n.

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