A353135 - OEIS

%I #17 May 14 2022 11:23:30

%S 3,5,10007,11777,12163,17291,20443,20477,37781,41333,47743,47777,

%T 49991,59887,59921,61091,61331,64271,77417,88177,88609,88643,89363,

%U 91639,93337,97073,105863,106453,107507,108463,108497,112363,113383,113717,125149,133631,134293

%N Primes having Fibonacci prime gaps to both neighbor primes.

%H Alois P. Heinz, <a href="/A353135/b353135.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 f:= proc(n) option remember; (t-> issqr(t+4) or issqr(t-4))(5*n^2) end:

%p q:= n-> isprime(n) and andmap(f, [n-prevprime(n), nextprime(n)-n]):

%p select(q, [$3..150000])[];

%t f[n_] := f[n] = With[{t = 5n^2}, IntegerQ@Sqrt[t+4] || IntegerQ@Sqrt[t-4]];

%t q[n_] := PrimeQ[n] && f[n-NextPrime[n, -1]] && f[NextPrime[n]-n];

%t Select[Range[3, 150000], q] (* _Jean-François Alcover_, May 14 2022, after _Alois P. Heinz_ *)

%Y Cf. A000040, A000045, A014445, A353088, A353136, A353137.

%K nonn

%O 1,1

%A _Alois P. Heinz_, Apr 25 2022