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A230138
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List of those primes p with p + 2 and 2*p - 5 both prime.
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5
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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}]
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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