A230227 Primes p with 3*p - 10 also prime.

5, 7, 11, 13, 17, 19, 23, 31, 37, 41, 47, 53, 59, 61, 67, 79, 83, 89, 97, 101, 107, 109, 131, 137, 151, 157, 163, 167, 173, 191, 193, 199, 223, 229, 251, 257, 269, 277, 283, 307, 313, 317, 331, 347, 353, 367, 373, 397, 401, 409

Offset

1,1

Comments

Conjecture: For any integer n > 4 not equal to 76, we have 2*n = p + q for some terms p and q from the sequence.

This is stronger than Goldbach's conjecture for even numbers.

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) = 5 since 3*5 - 10 = 5 is prime.

Mathematica

PQ[p_]:=PQ[p]=p>3&&PrimeQ[3p-10]
m=0
Do[If[PQ[Prime[n]], m=m+1; Print[m, " ", Prime[n]]], {n, 1, 80}]
Select[Prime[Range[100]], PrimeQ[3#-10]&] (* Harvey P. Dale, Jun 28 2015 *)

Crossrefs

Cf. A000040, A002375, A230138, A230140, A230141, A230217, A230219, A230223, A230224, A230230.

Sequence in context: A020589 A364001 A216523 * A101635 A118941 A096547

Adjacent sequences: A230224 A230225 A230226 * A230228 A230229 A230230

Keyword

nonn

Author

Zhi-Wei Sun, Oct 12 2013

Status

approved