A075133 -id:A075133

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A075134

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).

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9, 15, 128, 228, 417, 562, 1214, 1364, 2425, 3085, 5281, 8256, 8926, 9187, 9332, 12782, 14497, 14607, 16227, 18763, 19601, 21476, 29911, 36080, 36218, 37083, 38660, 40104, 40863, 42094, 44126, 46918, 48924, 49301, 53564, 56568, 62982, 64775, 66530, 68218

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OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..40.

EXAMPLE

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.

MATHEMATICA

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]]

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

CROSSREFS

Cf. A005385, A075133.

KEYWORD

nonn

AUTHOR

Zak Seidov, Sep 04 2002

EXTENSIONS

More terms from Harvey P. Dale, Jul 17 2011

STATUS

approved

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