A045378 -id:A045378 - cp's OEIS frontend

A045356 Primes congruent to {0, 2, 4} mod 5.

2, 5, 7, 17, 19, 29, 37, 47, 59, 67, 79, 89, 97, 107, 109, 127, 137, 139, 149, 157, 167, 179, 197, 199, 227, 229, 239, 257, 269, 277, 307, 317, 337, 347, 349, 359, 367, 379, 389, 397, 409, 419, 439, 449, 457, 467

Offset: 1

N. J. A. Sloane

A039703(A049084(a(n))) = even; complement of A045429. - Reinhard Zumkeller, Feb 25 2008

R. Zumkeller, Table of n, a(n) for n = 1..1001

Cf. A045370, A045378, A137977.

[ p: p in PrimesUpTo(1000) | p mod 5 in {0, 2, 4} ]; // Vincenzo Librandi, Aug 07 2012

Select[Prime[Range[400]], MemberQ[{0, 2, 4}, Mod[#, 5]] &] (* Vincenzo Librandi, Aug 07 2012 *)
Select[Prime[Range[100]], EvenQ[Mod[#, 5]] &]  (* Zak Seidov, Aug 31 2012 *)
Select[Flatten[#+{0,2,4}&/@(5*Range[0,100])],PrimeQ] (* Harvey P. Dale, Sep 14 2019 *)

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

Original entry on oeis.org

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

Zak Seidov, Dec 19 2012

nonn

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

			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.

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

Cf. A045378, A070689.

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

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

cp's OEIS Frontend

A045356 Primes congruent to {0, 2, 4} mod 5.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica