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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. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

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.

LINKS

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

FORMULA

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

EXAMPLE

F_7 = 13, ......01101 in binary.

F_8 = 21, ......10101 in binary.

--------------------------

Anded together: 00101

which has two 1-bits, thus a(7)=2.

PROG

(Scheme): (define (A219660 n) (A000120 (A051122 n)))

CROSSREFS

Cf. A000045 (Fibonacci numbers), A020909, A051122-A051124.

Sequence in context: A226207 A226324 A023604 * A060964 A118206 A029314

Adjacent sequences:  A219657 A219658 A219659 * A219661 A219662 A219663

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, Dec 03 2012

STATUS

approved

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Last modified December 7 22:29 EST 2019. Contains 329850 sequences. (Running on oeis4.)