A356964 Replace 2^k in binary expansion of n with tribonacci(k+3) (where tribonacci corresponds to A000073).

0, 1, 2, 3, 4, 5, 6, 7, 7, 8, 9, 10, 11, 12, 13, 14, 13, 14, 15, 16, 17, 18, 19, 20, 20, 21, 22, 23, 24, 25, 26, 27, 24, 25, 26, 27, 28, 29, 30, 31, 31, 32, 33, 34, 35, 36, 37, 38, 37, 38, 39, 40, 41, 42, 43, 44, 44, 45, 46, 47, 48, 49, 50, 51, 44, 45, 46, 47

Offset: 0

Author

Rémy Sigrist, Sep 06 2022

Keywords

• nonn
• base

Comments

This sequence is to tribonacci numbers (A000073) what A022290 is to Fibonacci numbers (A000045).

For any k >= 0, k appears A117546(k) times in this sequence.

Examples

			For n = 9:
- 9 = 2^3 + 2^0,
- so a(9) = A000073(3+3) + A000073(0+3) = 7 + 1 = 8.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192
• Index entries for sequences related to Zeckendorf expansion of n

Crossrefs

Cf. A000073, A003726, A003796, A022290, A117546.

Programs

PARI

a(n) = { my (v=0, k); while (n, n-=2^k=valuation(n,2); v+=([0,1,0; 0,0,1; 1,1,1]^(3+k))[2,1]); return (v); }

Python

def A356964(n):
    a, b, c, s = 1,2,4,0
    for i in bin(n)[-1:1:-1]:
        s += int(i)*a
        a, b, c = b, c, a+b+c
    return s # Chai Wah Wu, Sep 10 2022

Formula

a(A003726(n+1)) = n.

a(A003796(n+1)) = n.