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Primes of the form (p^2 + 9)/2 where p is prime.
0

%I #17 Oct 10 2021 15:19:51

%S 17,29,89,149,269,929,1109,1409,3449,5309,6389,8069,12329,14969,33029,

%T 34589,42929,47129,48989,60209,67349,78809,98129,109049,118589,136769,

%U 158489,175829,213209,264269,317609,338669,363809,367229,389849,438989,454109,467549

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

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

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

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

%t Select[(Select[Range[3, 1000], PrimeQ]^2 + 9)/2, PrimeQ] (* _Amiram Eldar_, Sep 05 2021 *)

%Y Cf. A000040, A045637, A062324.

%Y Subsequence of A076727 and of A103739.

%K nonn

%O 1,1

%A _Burak Muslu_, Sep 05 2021