A230138 List of those primes p with p + 2 and 2*p - 5 both prime.

5, 11, 17, 29, 59, 71, 101, 137, 149, 179, 197, 227, 281, 311, 431, 599, 617, 641, 809, 821, 857, 1151, 1277, 1319, 1451, 1481, 1487, 1607, 1667, 1697, 1997, 2027, 2081, 2111, 2129, 2339, 2657, 2711, 2789, 3167, 3329, 3371, 3461, 3557, 3767, 3917, 3929, 4049, 4217, 4259

Offset

1,1

Comments

Clearly, all terms are congruent to 5 modulo 6, and not congruent to 3 modulo 5. Primes in this sequence are sparser than twin primes and Sophie Germain primes.

This sequence is interesting because of the conjectures in the comments in A230140 and A230141.

Intersection of A001359 and A089253 (or A063909). - M. F. Hasler, Oct 10 2013

Links

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

Example

a(1) = 5 since neither 2 + 2 nor 2*3 - 5 is prime, but 5 + 2 = 7 and 2*5 - 5 = 5 are both prime.

Mathematica

PQ[p_]:=PQ[p]=PrimeQ[p+2]&&PrimeQ[2p-5]
m=0
Do[If[PQ[Prime[n]], m=m+1; Print[m, " ", Prime[n]]], {n, 1, 584}]

Prog

(PARI) is_A230138(p)=isprime(p)&&isprime(p+2)&&isprime(p*2-5) \\ For large p it might be much faster to check first whether p%6==5. - M. F. Hasler, Oct 10 2013

Crossrefs

Cf. A001359, A006512, A005384, A230140, A230141.

Sequence in context: A074267 A268518 A268521 * A231652 A321792 A068072

Adjacent sequences: A230135 A230136 A230137 * A230139 A230140 A230141

Keyword

nonn

Author

Zhi-Wei Sun, Oct 10 2013

Status

approved