Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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