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Fibonacci(Pn+1) mod Pn, where Pn is the n-th prime.
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%I #9 Nov 27 2015 12:26:11

%S 0,0,3,0,1,0,0,1,0,1,1,0,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,

%T 1,1,0,0,0,0,1,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,

%U 0,1,0,1,0,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0

%N Fibonacci(Pn+1) mod Pn, where Pn is the n-th prime.

%C Terms are 1 when Pn == 1 or 4 mod 5, terms are 0 when Pn == 2 or 3 mod 5.

%e P3=5, Fibonacci(5-1)=3 mod 5.

%t Table[Mod[Fibonacci[n+1],n],{n,Prime[Range[110]]}] (* _Harvey P. Dale_, Nov 27 2015 *)

%Y Cf. A000045, A003631, A045468, A051834, A051831.

%K nonn

%O 1,3

%A _Jud McCranie_, Dec 11 1999