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

1,2

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, ...

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000045, A000120, A011373.

A353987 is a subsequence.

Sequence in context: A026080 A071795 A059501 * A138049 A099387 A359095

Adjacent sequences: A353983 A353984 A353985 * A353987 A353988 A353989

Keyword

nonn,base

Author

Amiram Eldar, May 13 2022

Status

approved