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 A088551 Fibonacci winding number: the number of 'mod n' operations in one cycle of the Fibonacci sequence modulo n. 2

%I

%S 1,3,2,8,11,7,4,11,28,3,9,12,23,19,9,16,11,7,28,5,12,23,9,48,40,35,19,

%T 4,59,12,19,15,16,39,9,36,6,27,28,19,19,43,11,59,23,15,9,55,148,35,38,

%U 52,35,6,21,31,16,26,57,28,12,21,43,68,51,67,14,19,119,32,7,72,112,99,5,33

%N Fibonacci winding number: the number of 'mod n' operations in one cycle of the Fibonacci sequence modulo n.

%C If pi(n) is the n-th Pisano number (A001175) then a(n) is usually about pi(n)/2 - and in any case a(n) > pi(n)/4.

%H T. D. Noe, <a href="/A088551/b088551.txt">Table of n, a(n) for n=2..10000</a>

%H R. C. Johnson, <a href="http://www.dur.ac.uk/bob.johnson/fibonacci/">Fibonacci Numbers and Resources</a>.

%F n*a(n) = sum{k=1..A001175(n)} fibonacci(k) mod n. [From Mircea Merca, Jan 03 2011]

%e a(8)=4 because one cycle of the Fibonacci numbers modulo 8 is 0, 1, 1, 2, 3, 5; 0, 5, 5; 2, 7; 1; - including 4 'mod 8' operations, each marked with a semi-colon.

%Y Cf. A001175, A015134, A214300.

%K easy,nice,nonn

%O 2,2

%A R C Johnson (bob.johnson(AT)dur.ac.uk), Nov 19 2003

%E More terms from _T. D. Noe_

%E Edited by _Ray Chandler_, Oct 26 2006

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