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A230138
List of those primes p with p + 2 and 2*p - 5 both prime.
5
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
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
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Oct 10 2013
STATUS
approved