A347530 - OEIS

A347530

Primes of the form (p^2 + 9)/2 where p is prime.

17, 29, 89, 149, 269, 929, 1109, 1409, 3449, 5309, 6389, 8069, 12329, 14969, 33029, 34589, 42929, 47129, 48989, 60209, 67349, 78809, 98129, 109049, 118589, 136769, 158489, 175829, 213209, 264269, 317609, 338669, 363809, 367229, 389849, 438989, 454109, 467549

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OFFSET

1,1

COMMENTS

Each p is an odd number, so p^2 == 1 (mod 8), thus (p^2 + 9)/2 == 1 (mod 4).

LINKS

Table of n, a(n) for n=1..38.

EXAMPLE

17 is in the sequence as 17 = (p^2 + 9)/2 where p = 5 is prime.

29 is in the sequence as 29 = (p^2 + 9)/2 where p = 7 is prime.

MATHEMATICA

Select[(Select[Range[3, 1000], PrimeQ]^2 + 9)/2, PrimeQ] (* Amiram Eldar, Sep 05 2021 *)