A353986 - OEIS

%I #15 Jul 10 2024 15:09:14

%S 1,2,4,7,24,27,49,51,52,69,75,114,130,131,158,169,186,217,250,263,292,

%T 335,340,345,374,474,500,507,520,547,565,583,600,604,627,717,760,791,

%U 828,831,908,996,997,1011,1023,1061,1081,1114,1242,1641,1660,1763,1780

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

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

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

%H Amiram Eldar, <a href="/A353986/b353986.txt">Table of n, a(n) for n = 1..10000</a>

%e 1 is a term since A011373(1) = A011373(2) = 1.

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

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

%o (PARI) isok(k) = hammingweight(fibonacci(k)) == hammingweight(fibonacci(k+1)); \\ _Michel Marcus_, May 13 2022

%o (Python)

%o from itertools import islice

%o def A353986_gen(): # generator of terms

%o         a, b, k, ah = 1, 1, 1, 1

%o         while True:

%o             if ah == (bh := b.bit_count()):

%o                 yield k

%o             a, b, ah = b, a+b, bh

%o             k += 1

%o A353986_list = list(islice(A353986_gen(),30)) # _Chai Wah Wu_, May 13 2022

%Y Cf. A000045, A000120, A011373.

%Y A353987 is a subsequence.

%K nonn,base

%O 1,2

%A _Amiram Eldar_, May 13 2022