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 A230223 Primes p such that 3*p-4, 3*p-10, and 3*p-14 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 (list; graph; refs; listen; history; text; internal format)
 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}] 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

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Last modified August 18 09:28 EDT 2022. Contains 356204 sequences. (Running on oeis4.)