A353088 Primes having square prime gaps to both neighbor primes.

9551, 12889, 22193, 22307, 27143, 29917, 32261, 40423, 42863, 46807, 46993, 47981, 57637, 60041, 60493, 71597, 72613, 73819, 77137, 84263, 88427, 89153, 90583, 93463, 97463, 97613, 97883, 112543, 115057, 118931, 126307, 127877, 131321, 134093, 137873, 144883

Offset: 1

Author

Alois P. Heinz, Apr 22 2022

Keywords

• nonn

Examples

			Prime 9551 is a term, the gap to the previous prime 9547 is 4 and the gap to the next prime 9587 is 36 and both gaps are squares.
		

Links

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

Crossrefs

Intersection of A000040 and A353073.

Cf. A000290, A001223, A016742, A138198, A353135, A353136, A353137, A353550.

Programs

Maple

q:= n-> isprime(n) and andmap(issqr, [n-prevprime(n), nextprime(n)-n]):
select(q, [$3..200000])[];

Mathematica

q[n_] := PrimeQ[n] && IntegerQ@Sqrt[n-NextPrime[n, -1]] && IntegerQ@ Sqrt[NextPrime[n]-n];
Select[Range[3, 200000], q] (* Jean-François Alcover, May 14 2022, after Alois P. Heinz *)
Select[Prime[Range[2,15000]],AllTrue[{Sqrt[#-NextPrime[#,-1]],Sqrt[NextPrime[#]-#]},IntegerQ]&] (* Harvey P. Dale, Jan 22 2024 *)

Python

from itertools import islice
from sympy import nextprime, integer_nthroot
def A353088_gen(): # generator of terms
    p, q, g, h = 3, 5, True, False
    while True:
        if g and h:
            yield p
        p, q = q, nextprime(q)
        g, h = h, integer_nthroot(q-p,2)[1]
A353088_list = list(islice(A353088_gen(),30)) # Chai Wah Wu, Apr 22 2022