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A237183 Primes p with phi(p+1) - 1 and phi(p+1) + 1 both prime, where phi(.) is Euler's totient function.

%I A237183 #11 Mar 06 2014 09:56:20
%S A237183 7,11,13,17,37,41,53,61,97,151,181,197,227,233,251,269,277,397,433,
%T A237183 457,487,541,557,571,593,619,631,719,743,769,839,857,929,941,947,953,
%U A237183 1013,1021,1049,1061,1063,1201,1237,1277,1307,1321,1367,1481,1511,1549
%N A237183 Primes p with phi(p+1) - 1 and phi(p+1) + 1 both prime, where phi(.) is Euler's totient function.
%C A237183 According to part (i) of the conjecture in A237168, this sequence should have infinitely many terms.
%H A237183 Zhi-Wei Sun, <a href="/A237183/b237183.txt">Table of n, a(n) for n = 1..10000</a>
%e A237183 a(1) = 7 since 7, phi(7+1) - 1 = 3 and phi(7+1) + 1 = 5 are all prime, but phi(2+1) - 1 = phi(3+1) - 1 = phi(5+1) - 1 = 1 is not prime.
%t A237183 PQ[n_]:=PrimeQ[EulerPhi[n]-1]&&PrimeQ[EulerPhi[n]+1]
%t A237183 n=0;Do[If[PQ[Prime[k]+1],n=n+1;Print[n," ",Prime[k]]],{k,1,10000}]
%t A237183 Select[Prime[Range[300]],And@@PrimeQ[EulerPhi[#+1]+{1,-1}]&] (* _Harvey P. Dale_, Mar 06 2014 *)
%o A237183 (PARI) s=[]; forprime(p=2, 2000, if(isprime(eulerphi(p+1)-1) && isprime(eulerphi(p+1)+1), s=concat(s, p))); s \\ _Colin Barker_, Feb 04 2014
%Y A237183 Cf. A000010, A000040, A001359, A006512, A072281, A237127, A237130, A237168.
%K A237183 nonn
%O A237183 1,1
%A A237183 _Zhi-Wei Sun_, Feb 04 2014