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%I #26 Nov 26 2016 21:47:22
%S 1,2,0,6,1,12,16,1,22,1,1,36,1,42,46,52,1,1,66,1,72,1,82,1,96,1,102,
%T 106,1,112,126,1,136,1,1,1,156,162,166,172,1,1,1,192,196,1,1,222,226,
%U 1,232,1,1,1,256,262,1,1,276,1,282,292,306,1,312,316,1,336,346,1,352,1
%N a(n) = Fibonacci(prime(n)) mod prime(n), where prime(n) is the n-th prime.
%C Terms are 1 when prime(n) == 1 or 4 mod 5, terms are prime(n)-1 when prime(n) == 2 or 3 mod 5.
%C In general, it appears that Fibonacci(k*p) mod p = Fibonacci(k) or p-Fibonacci(k) for prime p > Fibonacci(k). For example Fibonacci(8*29) mod 29 = 21. - _Gary Detlefs_, May 28 2014
%H Alois P. Heinz, <a href="/A051831/b051831.txt">Table of n, a(n) for n = 1..20000</a>
%H R. Peele and P. Stanica, <a href="http://arxiv.org/abs/math/0010186">Matrix powers of column-justified Pascal triangles and Fibonacci sequences</a>, arXiv:math/0010186 [math.CO], 2000.
%e prime(3) = 5, fibonacci(5) = 5 == 0 mod 5.
%p p:= (M, n, k)-> map(x-> x mod k, `if`(n=0, <<1|0>, <0|1>>,
%p `if`(n::even, p(M, n/2, k)^2, p(M, n-1, k).M))):
%p a:= n-> p(<<0|1>, <1|1>>, ithprime(n)$2)[1, 2]:
%p seq(a(n), n=1..80); # _Alois P. Heinz_, Oct 10 2015
%t Mod[Fibonacci[Prime[#]],Prime[#]]&/@Range[75] (* _Harvey P. Dale_, Jan 14 2011 *)
%o (PARI) vector(80, n, fibonacci(prime(n)) % prime(n)) \\ _Michel Marcus_, Jul 15 2015
%Y Cf. A000045, A003631, A045468, A051834, A051830, A236395.
%K nonn
%O 1,2
%A _Jud McCranie_, Dec 11 1999
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