A384298 Primes p such that p + 4, p + 12 and p + 16 are also primes.

7, 67, 97, 487, 757, 1567, 1597, 2377, 3907, 7687, 8677, 12097, 12907, 13147, 14407, 14767, 15667, 16057, 19417, 21487, 31177, 38317, 43777, 52567, 57637, 58897, 65167, 65827, 67477, 67927, 74857, 81547, 90007, 90187, 93967, 94777, 95467, 95617, 102547, 111427, 112237, 114757, 123817, 129277

Offset

1,1

Comments

Initial members of prime quartets that correspond to the difference pattern [4, 8, 4].

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

a(n) == 7 (mod 30).

Example

p=97: 97+4=101, 97+12=109, 97+16=113 —> prime quartet: (97, 101, 109, 113).

Maple

q:= n-> andmap(i-> isprime(n+4*i), [0, 1, 3, 4]):
select(q, [7+30*i$i=0..4309])[];  # Alois P. Heinz, May 29 2025

Mathematica

Select[Prime[Range[12099]], AllTrue[#+{4, 12, 16}, PrimeQ]&] (* James C. McMahon, May 29 2025 *)

Crossrefs

Cf. A000040, A001223.

Cf. A136162 [2, 4, 2], A052378 [4, 2, 4], A382810 [6, 4, 6].

Sequence in context: A106111 A386083 A261184 * A142786 A139783 A103102

Adjacent sequences: A384295 A384296 A384297 * A384299 A384300 A384301

Keyword

nonn

Author

Alexander Yutkin, May 25 2025

Status

approved