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%I #14 Nov 15 2021 16:28:00
%S 11,23,47,167,359,719,1439,2039,2879,4079,4127,4919,5639,5807,5927,
%T 6047,7247,7559,7607,7727,9839,10799,11279,13799,13967,14159,15287,
%U 15647,20327,21599,21767,23399,24407,24527,25799,28319,28607,29399
%N Primes p such that (p-1)/2 and (p-3)/4 are also prime.
%C Call p "m-prime" iff (p-(2^i-1))/2^i is prime for i=0..m; sequence gives 2-primes. 0-primes are primes (A000040) and 1-primes are safe primes (A005385). a(n)-1 and a(n) are consecutive terms of the sequence A065966. It is not known if there are infinitely many m-primes for m > 0.
%H Harry J. Smith, <a href="/A066179/b066179.txt">Table of n, a(n) for n=1,...,1000</a>
%t lst={};Do[p=Prime[n];If[PrimeQ[a=(p-1)/2]&&PrimeQ[(a-1)/2],AppendTo[lst,p]],{n,8!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Feb 27 2009 *)
%o (PARI) { n=0; default(primelimit, 4294965247); for (m=1, 10^9, p=prime(m); if (frac((p-3)/4), next); if (isprime((p-3)/4) && isprime((p-1)/2), write("b066179.txt", n++, " ", p); if (n==1000, return)) ) } \\ _Harry J. Smith_, Feb 05 2010
%Y Cf. A000040, A005385, A065966.
%K nonn
%O 1,1
%A _Vladeta Jovovic_, Dec 14 2001
%E Offset changed from 0 to 1 by _Harry J. Smith_, Feb 05 2010