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

Author

Zak Seidov, Jan 22 2015

Keywords

• nonn

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

Crossrefs

Cf. A005098.

Programs

Magma

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

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 *)