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Nextprime(F(n)) - prevprime(F(n)), where F(n) is the n-th Fibonacci number.
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%I #10 Jul 29 2015 19:05:46

%S 3,4,4,6,4,6,6,14,10,10,6,6,8,18,12,24,16,10,6,12,30,12,24,42,30,24,

%T 60,24,30,34,30,36,46,12,36,18,34,24,24,30,36,52,72,16,22,48,44,50,34,

%U 20,20,28,44,50,40,92,60,86,16,52,48,66,46,168,50,174,36

%N Nextprime(F(n)) - prevprime(F(n)), where F(n) is the n-th Fibonacci number.

%C Smallest prime following Fibonacci(n) minus largest prime immediately preceding Fibonacci(n). Starting from Fibonacci(4), because for n<4 there is no prime preceding Fibonacci(n).

%H Alois P. Heinz, <a href="/A182487/b182487.txt">Table of n, a(n) for n = 4..1000</a>

%F a(n) = A014208(n+4) - A180422(n).

%e a(0) = A014208(4) - A180422(0) = 5 - 2 = 3,

%e a(7) = A014208(11) - A180422(7) = 97-83 = 14.

%p a:= n-> (f-> nextprime(f)-prevprime(f))(combinat[fibonacci](n)):

%p seq(a(n), n=4..100); # _Alois P. Heinz_, Jul 29 2015

%t Table[f = Fibonacci[n]; NextPrime[f] - NextPrime[f, -1], {n, 4, 100}] (* _T. D. Noe_, May 02 2012 *)

%Y Cf. A014208, A180422, A013633, A058043, A058054, A161503.

%Y Cf. A079677 (distance from F(n) to the nearest prime).

%K nonn,easy

%O 4,1

%A _Alex Ratushnyak_, May 02 2012