This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A113188 #12 Aug 04 2024 13:09:13
%S A113188 2,3,5,7,11,13,19,29,31,47,53,89,131,139,199,233,521,607,953,1453,
%T A113188 1597,2207,2351,2579,3571,6763,9349,10891,28513,28649,28657,42187,
%U A113188 44771,46279,75017,189653,317777,514229,1981891,2177699,3010349,3206767
%N A113188 Primes that are the difference of two Fibonacci numbers; primes in A007298.
%C A113188 The difference F(i)-F(j) equals the sum F(j-1)+...+F(i-2) [Corrected by _Patrick Capelle_, Mar 01 2008]. In general, we need gcd(i,j)=1 for F(i)-F(j) to be prime. The exceptions are handled by the following rule: if i and j are both even or both odd, then F(i)-F(j) is prime if either (1) i-j=4 and L(i-2) is a Lucas prime or (2) i-j=2 and F(i-1) is a Fibonacci prime.
%H A113188 T. D. Noe, <a href="/A113188/b113188.txt">Table of n, a(n) for n = 1..1000</a>
%e A113188 The prime 139 is here because it is F(12)-F(5).
%t A113188 lst={}; Do[p=Fibonacci[n]-Fibonacci[i]; If[PrimeQ[p], AppendTo[lst, p]], {n, 2, 40}, {i, n-1}]; Union[lst]
%t A113188 Select[Union[Flatten[Differences/@Subsets[Fibonacci[Range[50]],{2}]]],PrimeQ] (* _Harvey P. Dale_, Aug 04 2024 *)
%o A113188 (PARI) list(lim)=my(v=List(),F=vector(A130233(lim),i,fibonacci(i)),s,t); for(i=1,#F, s=0; forstep(j=i,1,-1, s+=F[j]; if(s>lim, break); if(isprime(s), listput(v,s)))); Set(v) \\ _Charles R Greathouse IV_, Oct 07 2016
%Y A113188 Cf. A000045 (Fibonacci numbers), A001605 (Fibonacci(n) is prime), A001606 (Lucas(n) is prime), A113189 (number of times that Fibonacci(n)-Fibonacci(i) is prime for i=0..n-3).
%K A113188 nonn
%O A113188 1,1
%A A113188 _T. D. Noe_, Oct 17 2005