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

1,1

Links

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A138154 A333269 A319598 * A126334 A068635 A156695

Adjacent sequences: A353132 A353133 A353134 * A353136 A353137 A353138

Keyword

nonn

Author

Alois P. Heinz, Apr 25 2022

Status

approved