A076727 -id:A076727 - cp's OEIS frontend

A224870 Numbers m such that m^2 + (m+3)^2 is prime.

1, 2, 5, 7, 10, 11, 16, 20, 22, 25, 37, 40, 41, 46, 50, 55, 61, 62, 65, 77, 85, 91, 92, 101, 106, 107, 116, 122, 125, 127, 130, 131, 142, 145, 146, 152, 155, 161, 172, 181, 182, 187, 196, 197, 206, 220, 221, 232, 235, 241, 242, 257, 260, 262, 265, 271, 275, 280, 281, 286, 295, 310, 317, 325, 326, 346, 356, 362, 380, 382, 386, 391

Offset: 1

Zak Seidov, Jul 22 2013

nonn

Zak Seidov, Table of n, a(n) for n = 1..1000

Cf. A027861, A027862, A076727.

A224870:=n->`if`(isprime(n^2 + (n+3)^2), n, NULL): seq(A224870(n), n=1..10^3); # Wesley Ivan Hurt, Feb 11 2017

k = 3; Select[Range[500], PrimeQ[#^2 + (# + k)^2]&]

isok(n) = isprime(n^2 + (n+3)^2); \\ Michel Marcus, Feb 13 2017

a(n) = (1/2)*(sqrt(2*A076727(n) - k^2) - k), k = 3.

A347530 Primes of the form (p^2 + 9)/2 where p is prime.

Original entry on oeis.org

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

Offset: 1

Burak Muslu, Sep 05 2021

nonn

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

			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.

Cf. A000040, A045637, A062324.

Subsequence of A076727 and of A103739.

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

cp's OEIS Frontend

A224870 Numbers m such that m^2 + (m+3)^2 is prime.

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