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A step cyclic recursion: a(n) = If[a(n - 1) - Prime[n] > 0, Abs[a(n - 1) - 2*n], If[a[n - 1] - Prime[n] < 0, Abs[a(n - 1) + 2*n], Fibonacci[n] - a(n - 1)]].
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%I #3 Mar 30 2012 17:34:27

%S 0,1,5,-3,5,15,3,17,33,15,35,13,37,63,35,65,33,67,31,69,109,67,111,65,

%T 113,63,115,61,117,59,119,181,117,183,115,185,113,187,111,189,109,191,

%U 107,193,701408540,701408450,701408358,701408264,701408168,701408070,701407970

%N A step cyclic recursion: a(n) = If[a(n - 1) - Prime[n] > 0, Abs[a(n - 1) - 2*n], If[a[n - 1] - Prime[n] < 0, Abs[a(n - 1) + 2*n], Fibonacci[n] - a(n - 1)]].

%F a(n) = If[a(n - 1) - Prime[n] > 0, Abs[a(n - 1) - 2*n], If[a[n - 1] - Prime[n] < 0, Abs[a(n - 1) + 2*n], Fibonacci[n] - a(n - 1)]].

%t a[0] = 0; a[1] = 1; a[n_] := a[n] = If[a[n - 1] - Prime[n] > 0, Abs[a[n - 1] - 2*n], If[a[n - 1] - Prime[n] < 0, Abs[a[n - 1] + 2*n], Fibonacci[n] - a[n - 1]]]; Table[a[n], {n, 0, 50}]

%K uned,sign

%O 1,3

%A _Roger L. Bagula_, Oct 01 2008