A254010 Numbers k such that 4k+1 and 4(k+1)+1 are primes.

3, 9, 24, 27, 48, 57, 69, 78, 87, 99, 114, 153, 168, 189, 192, 213, 219, 234, 252, 273, 303, 324, 357, 372, 387, 399, 402, 423, 468, 498, 534, 567, 573, 594, 597, 609, 618, 654, 672, 687, 699, 708, 714, 738, 759, 804, 813, 864, 882, 903, 918, 924, 948, 969, 1032, 1038, 1128, 1182, 1197, 1203, 1233, 1242, 1269, 1308, 1353

Offset

1,1

Comments

Both k and k+1 are terms in A005098. All terms are multiples of 3.

4k+1 and 4(k+1)+1 are pairs of consecutive primes. Notice that in all cases, the numbers 4(k-1)+1 and 4(k+2)+1 are not prime as they are multiples of 3.

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Maple

A254010:=n->`if`(isprime(4*n+1) and isprime(4*(n+1)+1), n, NULL): seq(A254010(n), n=1..2000); # Wesley Ivan Hurt, Apr 23 2015

Mathematica

Select[Range[1000], PrimeQ[4 # + 1] && PrimeQ[4 (# + 1) + 1] &] (* Vincenzo Librandi, Apr 24 2015 *)

Prog

(Magma) [n: n in [0..1000] | IsPrime(4*n+1) and IsPrime(4*(n+1)+1)]; // Vincenzo Librandi, Apr 24 2015

Crossrefs

Cf. A005098.

Sequence in context: A129834 A029488 A198681 * A338124 A024314 A120012

Adjacent sequences: A254007 A254008 A254009 * A254011 A254012 A254013

Keyword

nonn

Author

Zak Seidov, Jan 22 2015

Status

approved