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%I #15 Jul 22 2023 16:37:08
%S 0,1,0,1,1,0,1,2,0,2,2,1,1,4,2,3,4,3,1,4,3,1,5,4,3,3,5,7,8,4,4,3,4,8,
%T 5,4,6,6,4,7,7,10,7,11,7,8,8,4,8,12,8,9,7,8,10,13,8,8,10,8,6,12,11,12,
%U 13,10,8,7,10,13,9,9,14,12,11,9,11,13,13,13
%N a(n) = number of bit-positions where Fibonacci numbers F(n) and F(n+1) contain both an 1-bit in their binary representation.
%C This sequence gives the number of "first-level" carries produced when computing Fibonacci numbers in binary arithmetic. that is, the carry-1-bits produced at the positions where the both summands F(n) and F(n+1) have 1-bits in the same bit-positions. This sum doesn't include any additional carries produced, when a produced carry-bit is added to an existing 1 at its left side.
%H Antti Karttunen, <a href="/A219660/b219660.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = A000120(A051122(n)).
%e F_7 = 13, ......01101 in binary.
%e F_8 = 21, ......10101 in binary.
%e --------------------------
%e Anded together: 00101
%e which has two 1-bits, thus a(7)=2.
%t a[n_] := DigitCount[BitAnd[Fibonacci[n], Fibonacci[n+1]], 2, 1]; Array[a, 100, 0] (* _Amiram Eldar_, Jul 22 2023 *)
%o (Scheme): (define (A219660 n) (A000120 (A051122 n)))
%Y Cf. A000045 (Fibonacci numbers), A020909, A051122, A051123, A051124.
%K nonn,base
%O 0,8
%A _Antti Karttunen_, Dec 03 2012
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