This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A219660 #20 Jul 17 2025 14:45:06 %S A219660 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 A219660 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 A219660 13,10,8,7,10,13,9,9,14,12,11,9,11,13,13,13 %N A219660 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 A219660 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 A219660 Antti Karttunen, <a href="/A219660/b219660.txt">Table of n, a(n) for n = 0..1000</a> %F A219660 a(n) = A000120(A051122(n)). %e A219660 F_7 = 13, ......01101 in binary. %e A219660 F_8 = 21, ......10101 in binary. %e A219660 -------------------------- %e A219660 Anded together: 00101 %e A219660 which has two 1-bits, thus a(7)=2. %t A219660 a[n_] := DigitCount[BitAnd[Fibonacci[n], Fibonacci[n+1]], 2, 1]; Array[a, 100, 0] (* _Amiram Eldar_, Jul 22 2023 *) %o A219660 (Scheme) (define (A219660 n) (A000120 (A051122 n))) %Y A219660 Cf. A000045 (Fibonacci numbers), A000120, A020909, A051122, A051123, A051124. %K A219660 nonn,base %O A219660 0,8 %A A219660 _Antti Karttunen_, Dec 03 2012