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A286296 a(n) = nextprime(P(n)+2) - P(n), where P(n) = Product_{k=1..n} Fibonacci(k) and nextprime(i) is the smallest prime > i.

%I A286296 #13 Jun 01 2017 13:19:12
%S A286296 4,4,3,5,7,11,17,17,37,23,47,37,29,19,47,59,19,37,71,59,31,67,239,101,
%T A286296 739,409,43,367,167,251,73,71,419,1567,107,83,223,191,227,449,97,173,
%U A286296 103,523,79,137,223,1163,661,103,103,541,227,2383,433,71,1069,643,251,163
%N A286296 a(n) = nextprime(P(n)+2) - P(n), where P(n) = Product_{k=1..n} Fibonacci(k) and nextprime(i) is the smallest prime > i.
%H A286296 Harry J. Smith, <a href="/A286296/b286296.txt">Table of n, a(n) for n = 1..169</a> [Based on b-file for A066889]
%p A286296 with(combinat);
%p A286296 F:=fibonacci;
%p A286296 P:=n->mul(F(i),i=1..n);
%p A286296 [seq(nextprime(P(n)+2)-P(n),n=1..100)];
%t A286296 NextPrime[#+2]-#&/@FoldList[Times,Fibonacci[Range[60]]] (* _Harvey P. Dale_, Jun 01 2017 *)
%Y A286296 A066889 is closely related (it is the same except for the first two terms).
%Y A286296 Cf. A000045.
%K A286296 nonn
%O A286296 1,1
%A A286296 _Harvey P. Dale_ and _N. J. A. Sloane_, May 31 2017