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A353986
Numbers k such that Fibonacci(k) and Fibonacci(k+1) have the same binary weight (A000120).
4
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
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
A353987 is a subsequence.
Sequence in context: A026080 A071795 A059501 * A138049 A099387 A359095
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, May 13 2022
STATUS
approved