A383396 Primes p such that p + 6, p + 10, p + 12, p + 16 and p + 22 are also primes.

7, 31, 2677, 35521, 42451, 44257, 55807, 93481, 118891, 198817, 221707, 234181, 313981, 393571, 560227, 669847, 1107781, 1210387, 1596367, 1616611, 1738411, 2710921, 3194551, 3377587, 3441931, 3484561, 3586537, 3699181, 3887551, 3904897, 4095661, 4192261, 4239721

Offset

1,1

Comments

Initial members of prime sextuples that correspond to the difference pattern [6, 4, 2, 4, 6].

Links

Table of n, a(n) for n=1..33.

Formula

a(n) == 1 (mod 6).

Example

p = 2677: 2677 + 6 = 2683, 2677 + 10 = 2687, 2677 + 12 = 2689, 2677 + 16 = 2693, 2677 + 22 = 2699 -> prime sextuple: (2677, 2683, 2687, 2689, 2693, 2699).

Mathematica

Select[Prime[Range[298900]], AllTrue[#+{6, 10, 12, 16, 22}, PrimeQ]&] (* James C. McMahon, May 02 2025 *)

Crossrefs

Cf. A000040, A001223.

Cf. A052378 [4, 2, 4], A022008 [4, 2, 4, 2, 4].

Sequence in context: A253640 A191297 A134709 * A139314 A290969 A163083

Adjacent sequences: A383393 A383394 A383395 * A383397 A383398 A383399

Keyword

nonn

Author

Alexander Yutkin, Apr 25 2025

Status

approved