A230223 Primes p such that 3*p-4, 3*p-10, and 3*p-14 are all prime.

7, 11, 17, 19, 31, 37, 47, 59, 79, 107, 131, 151, 157, 229, 317, 367, 409, 431, 479, 499, 521, 541, 739, 787, 1031, 1181, 1307, 1381, 1487, 1601, 1697, 1747, 1951, 2551, 2749, 2767, 2917, 3251, 3391, 3449, 3581, 3931, 4217, 4349, 4447, 4567, 4639, 4721, 4909, 4967

Offset

1,1

Comments

Conjecture: Any even number greater than 35 can be written as a sum of four terms of this sequence.

Primes in the sequence should be sparser than twin primes although this has not been proved.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Zhi-Wei Sun, Conjectures involving primes and quadratic forms, preprint, arXiv:1211.1588.

Example

a(1) = 7 since 3*7-4 = 17, 3*7-10 = 11 and 3*7-14 = 7 are prime.

Mathematica

RQ[n_]:=n>5&&PrimeQ[3n-4]&&PrimeQ[3n-10]&&PrimeQ[3n-14]
m=0
Do[If[RQ[Prime[n]], m=m+1; Print[m, " ", Prime[n]]], {n, 1, 1000}]
Select[Prime[Range[700]], AllTrue[3#-{4, 10, 14}, PrimeQ]&] (* Harvey P. Dale, Sep 29 2023 *)

Prog

(PARI) is(p)=isprime(p) && isprime(3*p-4) && isprime(3*p-10) && isprime(3*p-14) \\ Charles R Greathouse IV, Oct 12 2013

Crossrefs

Cf. A023201, A046131, A230138, A230140, A230217, A230219, A230224.

Sequence in context: A155048 A296926 A063639 * A309587 A339954 A260893

Adjacent sequences: A230220 A230221 A230222 * A230224 A230225 A230226

Keyword

nonn

Author

Zhi-Wei Sun, Oct 12 2013

Status

approved