

A230223


Primes p such that 3*p4, 3*p10, and 3*p14 are all prime.


13



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
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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

ZhiWei Sun, Table of n, a(n) for n = 1..10000
ZhiWei Sun, Conjectures involving primes and quadratic forms, preprint, arXiv:1211.1588.


EXAMPLE

a(1) = 7 since 3*74 = 17, 3*710 = 11 and 3*714 = 7 are prime.


MATHEMATICA

RQ[n_]:=n>5&&PrimeQ[3n4]&&PrimeQ[3n10]&&PrimeQ[3n14]
m=0
Do[If[RQ[Prime[n]], m=m+1; Print[m, " ", Prime[n]]], {n, 1, 1000}]


PROG

(PARI) is(p)=isprime(p) && isprime(3*p4) && isprime(3*p10) && isprime(3*p14) \\ 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

ZhiWei Sun, Oct 12 2013


STATUS

approved



