login
A353135
Primes having Fibonacci prime gaps to both neighbor primes.
5
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 25 2022
STATUS
approved