A353986 Numbers k such that Fibonacci(k) and Fibonacci(k+1) have the same binary weight (A000120).

1, 2, 4, 7, 24, 27, 49, 51, 52, 69, 75, 114, 130, 131, 158, 169, 186, 217, 250, 263, 292, 335, 340, 345, 374, 474, 500, 507, 520, 547, 565, 583, 600, 604, 627, 717, 760, 791, 828, 831, 908, 996, 997, 1011, 1023, 1061, 1081, 1114, 1242, 1641, 1660, 1763, 1780

Offset: 1

Author

Amiram Eldar, May 13 2022

Keywords

• nonn
• base

Comments

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

The corresponding values of A011373(k) are 1, 1, 2, 3, 6, 11, 18, 17, 17, 23, 23, 43, 42, 42, 51, ...

Examples

			1 is a term since A011373(1) = A011373(2) = 1.
4 is a term since A011373(4) = A011373(5) = 2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000045, A000120, A011373.

A353987 is a subsequence.

Programs

Mathematica

s[n_] := s[n] = DigitCount[Fibonacci[n], 2, 1]; Select[Range[2000], s[#] == s[# + 1] &]

PARI

isok(k) = hammingweight(fibonacci(k)) == hammingweight(fibonacci(k+1)); \\ Michel Marcus, May 13 2022

Python

from itertools import islice
def A353986_gen(): # generator of terms
        a, b, k, ah = 1, 1, 1, 1
        while True:
            if ah == (bh := b.bit_count()):
                yield k
            a, b, ah = b, a+b, bh
            k += 1
A353986_list = list(islice(A353986_gen(),30)) # Chai Wah Wu, May 13 2022