

A219660


a(n) = number of bitpositions where Fibonacci numbers F(n) and F(n+1) contain both an 1bit 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
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OFFSET

0,8


COMMENTS

This sequence gives the number of "firstlevel" carries produced when computing Fibonacci numbers in binary arithmetic. that is, the carry1bits produced at the positions where the both summands F(n) and F(n+1) have 1bits in the same bitpositions. This sum doesn't include any additional carries produced, when a produced carrybit 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 1bits, thus a(7)=2.


PROG

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


CROSSREFS

Cf. A000045 (Fibonacci numbers), A020909, A051122A051124.
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



