A353135 Primes having Fibonacci prime gaps to both neighbor primes.

3, 5, 10007, 11777, 12163, 17291, 20443, 20477, 37781, 41333, 47743, 47777, 49991, 59887, 59921, 61091, 61331, 64271, 77417, 88177, 88609, 88643, 89363, 91639, 93337, 97073, 105863, 106453, 107507, 108463, 108497, 112363, 113383, 113717, 125149, 133631, 134293

Offset: 1

Author

Alois P. Heinz, Apr 25 2022

Keywords

• nonn

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Maple

f:= proc(n) option remember; (t-> issqr(t+4) or issqr(t-4))(5*n^2) end:
q:= n-> isprime(n) and andmap(f, [n-prevprime(n), nextprime(n)-n]):
select(q, [$3..150000])[];

Mathematica

f[n_] := f[n] = With[{t = 5n^2}, IntegerQ@Sqrt[t+4] || IntegerQ@Sqrt[t-4]];
q[n_] := PrimeQ[n] && f[n-NextPrime[n, -1]] && f[NextPrime[n]-n];
Select[Range[3, 150000], q] (* Jean-François Alcover, May 14 2022, after Alois P. Heinz *)