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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).

%I A353987 #21 Aug 12 2025 12:41:39
%S A353987 1,51,130,996,3224,4287,9951,12676,72004,53812945,141422620
%N 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).
%C A353987 Numbers k such that A011373(k) = A011373(k+1) = A011373(k+2).
%C A353987 The corresponding values of A011373(k) are 1, 17, 42, 354, 1110, 1490, 3451, 4383, 24988, 18678035, ...
%e A353987 1 is a term since A011373(1) = A011373(2) = A011373(3) = 1.
%e A353987 51 is a term since A011373(51) = A011373(52) = A011373(53) = 17.
%t A353987 s[n_] := s[n] = DigitCount[Fibonacci[n], 2, 1]; Select[Range[10^4], s[#] == s[# + 1] == s[# + 2] &]
%o A353987 (PARI) hf(k) = hammingweight(fibonacci(k)); \\ A011373
%o A353987 isok(k) = my(h=hf(k)); (h == hf(k+1)) && (h == hf(k+2)); \\ _Michel Marcus_, May 13 2022
%o A353987 (Python)
%o A353987 # if Python version < 3.10, replace c.bit_count() with bin(c).count('1')
%o A353987 from itertools import islice
%o A353987 def A353987_gen(): # generator of terms
%o A353987         b, c, k, ah, bh = 1, 2, 1, 1, 1
%o A353987         while True:
%o A353987             if ah == (ch := c.bit_count()) == bh:
%o A353987                 yield k
%o A353987             b, c, ah, bh = c, b+c, bh, ch
%o A353987             k += 1
%o A353987 A353987_list = list(islice(A353987_gen(),7)) # _Chai Wah Wu_, May 14 2022
%Y A353987 Cf. A000045, A000120, A011373.
%Y A353987 Subsequence of A353986.
%K A353987 nonn,base,more
%O A353987 1,2
%A A353987 _Amiram Eldar_, May 13 2022
%E A353987 a(11) from _Dennis Yurichev_, Jul 10 2024