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%I #11 Nov 15 2021 16:44:06
%S 23,47,719,1439,2879,4079,9839,11279,21599,28319,51599,84719,92399,
%T 95279,96959,137279,157679,159119,178799,209519,219839,243119,349199,
%U 429119,430799,441839,462719,481199,491279,507359,533999,571199,597599
%N Triple-safe primes p: p, (p-1)/2, (p-3)/4, and (p-7)/8 are all prime.
%C These occur in a proof of nonexistence of a certain type of permutation group for p (Theorem 8 by Ito). - _R. J. Mathar_, May 29 2011
%H Noboru Ito, <a href="http://dx.doi.org/10.1090/S0002-9904-1963-10904-0">Transitive permutation groups of degree p=2q+1, p and q being prime numbers</a>, Bull. AMS 69 (2) (1963), 165-192.
%F a(n) >> n log^(4) n. - _Charles R Greathouse IV_, Oct 14 2021
%e (23-1)/2=11, (11-1)/2=5, (5-1)/2=2(prime), ...
%t lst={};Do[p=Prime[n];If[PrimeQ[a=(p-1)/2]&&PrimeQ[b=(a-1)/2]&&PrimeQ[(b-1)/2],AppendTo[lst,p]],{n,9!}];lst
%o (PARI) is(n)=n%8==7 && isprime(n) && isprime(n\2) && isprime(n\4) && isprime(n\8) \\ _Charles R Greathouse IV_, Oct 14 2021
%o (PARI) list(lim)=my(v=List()); forprimestep(p=23,lim\1,8, if(isprime(p\8) && isprime(p\4) && isprime(p\2), listput(v,p))); Vec(v); \\ _Charles R Greathouse IV_, Oct 14 2021
%Y Cf. A005385, A066179, A157357.
%K nonn,easy
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Feb 27 2009
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