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 A353135 #17 May 14 2022 11:23:30
%S A353135 3,5,10007,11777,12163,17291,20443,20477,37781,41333,47743,47777,
%T A353135 49991,59887,59921,61091,61331,64271,77417,88177,88609,88643,89363,
%U A353135 91639,93337,97073,105863,106453,107507,108463,108497,112363,113383,113717,125149,133631,134293
%N A353135 Primes having Fibonacci prime gaps to both neighbor primes.
%H A353135 Alois P. Heinz, <a href="/A353135/b353135.txt">Table of n, a(n) for n = 1..10000</a>
%e A353135 Prime 10007 is a term, the gap to the previous prime 9973 is 34 and the gap to the next prime 10009 is 2 and both gaps are Fibonacci numbers.
%p A353135 f:= proc(n) option remember; (t-> issqr(t+4) or issqr(t-4))(5*n^2) end:
%p A353135 q:= n-> isprime(n) and andmap(f, [n-prevprime(n), nextprime(n)-n]):
%p A353135 select(q, [$3..150000])[];
%t A353135 f[n_] := f[n] = With[{t = 5n^2}, IntegerQ@Sqrt[t+4] || IntegerQ@Sqrt[t-4]];
%t A353135 q[n_] := PrimeQ[n] && f[n-NextPrime[n, -1]] && f[NextPrime[n]-n];
%t A353135 Select[Range[3, 150000], q] (* _Jean-François Alcover_, May 14 2022, after _Alois P. Heinz_ *)
%Y A353135 Cf. A000040, A000045, A014445, A353088, A353136, A353137.
%K A353135 nonn
%O A353135 1,1
%A A353135 _Alois P. Heinz_, Apr 25 2022