%I #12 Nov 21 2013 12:47:53

%S 9,15,128,228,417,562,1214,1364,2425,3085,5281,8256,8926,9187,9332,

%T 12782,14497,14607,16227,18763,19601,21476,29911,36080,36218,37083,

%U 38660,40104,40863,42094,44126,46918,48924,49301,53564,56568,62982,64775,66530,68218

%N Indices of triple-safe primes: p=prime(n) is double-safe: q=(p-1)/2, r=(q-1)/2 and s=(r-1)/2 are all prime (and q is double-safe).

%C prime p is safe if q=(p-1)/2 is prime, so p is double safe if also r=(q-1)/2 is prime. So p is triple-safe if q is double safe Safe primes are in A005385, indices of double-safe primes are in A075133

%e 15 is a member because p(15)=47, q=(p-1)/2=23, r=(q-1)2=11 and s=(r-1)=5 are primes.

%t se3=Select[(Select[(Select[(Prime[Range[30000]]-1)/2, PrimeQ]-1)/2, PrimeQ]-1)/2, PrimeQ]; Map[PrimePi, Map[2(2(2*#+1)+1)+1&, se3]]

%t tspQ[n_]:=And@@PrimeQ[NestList[(#-1)/2&,Prime[n],3]]; Select[ Range[ 100000], tspQ] (* _Harvey P. Dale_, Jul 17 2011 *)

%Y Cf. A005385, A075133.

%K nonn

%O 1,1

%A _Zak Seidov_, Sep 04 2002

%E More terms from Harvey P. Dale, Jul 17 2011