A192794 Numbers k such that k + 2 and k^2 + 4 are primes.

1, 3, 5, 15, 17, 27, 35, 45, 57, 65, 87, 95, 125, 135, 137, 147, 155, 177, 255, 267, 275, 347, 357, 407, 447, 455, 477, 507, 605, 615, 707, 717, 755, 767, 785, 795, 827, 837, 905, 935, 945, 1185, 1235, 1247, 1257, 1275, 1325, 1365, 1457, 1497, 1595, 1695

Offset: 1

Author

Zak Seidov, Dec 19 2012

Keywords

• nonn

Comments

a(n) is odd for all n. For n > 2, the last digit of a(n) is either 5 or 7 because for n == 1, 3, 9 mod 10, either n+2 == 5 (mod 10) or n^2+4 == 5 (mod 10). Thus if m>1 is a term, then m+2 is in A045378. - Chai Wah Wu, Sep 06 2020

Examples

			1 + 2 = 3 and  1 + 4 = 5 are primes,
3 + 2 = 5 and  9 + 4 = 13 are primes,
5 + 2 = 7 and 25 + 4 = 29 are primes.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A045378, A070689.

Programs

Maple

filter:= n -> isprime(n+2) and isprime(n^2+4):
select(filter, [seq(i,i=1..2000,2)]); # Robert Israel, Nov 11 2023

PARI

{a=2;forstep(n=1,2000,2,if(isprime(n+a)&&isprime(n^2+a^2), print1(n",")))}