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.

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, 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, 13, 10, 8, 7, 10, 13, 9, 9, 14, 12, 11, 9, 11, 13, 13, 13

Offset: 0

Author

Antti Karttunen, Dec 03 2012

Keywords

• nonn
• base

Comments

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.

Examples

			F_7 = 13, ......01101 in binary.
F_8 = 21, ......10101 in binary.
--------------------------
Anded together: 00101
which has two 1-bits, thus a(7)=2.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000045 (Fibonacci numbers), A000120, A020909, A051122, A051123, A051124.

Programs

Mathematica

a[n_] := DigitCount[BitAnd[Fibonacci[n], Fibonacci[n+1]], 2, 1]; Array[a, 100, 0] (* Amiram Eldar, Jul 22 2023 *)

Scheme

(define (A219660 n) (A000120 (A051122 n)))

Formula

a(n) = A000120(A051122(n)).