A353987 Numbers k such that F(k), F(k+1) and F(k+2) have the same binary weight (A000120), where F(k) is the k-th Fibonacci number (A000045).

1, 51, 130, 996, 3224, 4287, 9951, 12676, 72004, 53812945, 141422620

Offset: 1

Author

Amiram Eldar, May 13 2022

Keywords

• nonn
• base
• more

Comments

Numbers k such that A011373(k) = A011373(k+1) = A011373(k+2).

The corresponding values of A011373(k) are 1, 17, 42, 354, 1110, 1490, 3451, 4383, 24988, 18678035, ...

Examples

			1 is a term since A011373(1) = A011373(2) = A011373(3) = 1.
51 is a term since A011373(51) = A011373(52) = A011373(53) = 17.
		

Crossrefs

Cf. A000045, A000120, A011373.

Subsequence of A353986.

Programs

Mathematica

s[n_] := s[n] = DigitCount[Fibonacci[n], 2, 1]; Select[Range[10^4], s[#] == s[# + 1] == s[# + 2] &]

PARI

hf(k) = hammingweight(fibonacci(k)); \\ A011373
isok(k) = my(h=hf(k)); (h == hf(k+1)) && (h == hf(k+2)); \\ Michel Marcus, May 13 2022

Python

# if Python version < 3.10, replace c.bit_count() with bin(c).count('1')
from itertools import islice
def A353987_gen(): # generator of terms
        b, c, k, ah, bh = 1, 2, 1, 1, 1
        while True:
            if ah == (ch := c.bit_count()) == bh:
                yield k
            b, c, ah, bh = c, b+c, bh, ch
            k += 1
A353987_list = list(islice(A353987_gen(),7)) # Chai Wah Wu, May 14 2022

Extensions

a(11) from Dennis Yurichev, Jul 10 2024