A075133 - OEIS

A075133

Indices of double-safe primes: p=prime(n) is double-safe: q=(p-1)/2 & r=(q-1)/2 are both prime (and q is safe).

5, 9, 15, 39, 72, 128, 228, 309, 417, 562, 567, 657, 740, 762, 779, 789, 927, 959, 967, 981, 1214, 1315, 1364, 1632, 1650, 1667, 1785, 1825, 2295, 2425, 2442, 2607, 2709, 2721, 2840, 3085, 3114, 3194, 3401, 3812, 3911, 4428, 4472, 4479, 4645, 4753, 4780

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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. Safe primes are in A005385, indices of triple-safe primes are in A075314

LINKS

Table of n, a(n) for n=1..47.

EXAMPLE

72 is a member because p(72)=359, q=(p-1)/2=179 and r=(q-1)2=89 are primes.

MATHEMATICA

se2=Select[(Select[(Prime[Range[20000]]-1)/2, PrimeQ]-1)/2, PrimeQ]; Map[PrimePi, Map[2(2*#+1)+1&, se2]]

dspQ[n_]:=Module[{q=(n-1)/2}, AllTrue[{q, (q-1)/2}, PrimeQ]]; Position[ Prime[ Range[5000]], _?(dspQ[#]&)]//Flatten (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 23 2016 *)

CROSSREFS

Cf. A005385, A075314.

Sequence in context: A062516 A249331 A345953 * A351826 A066081 A076856

Adjacent sequences: A075130 A075131 A075132 * A075134 A075135 A075136

KEYWORD

nonn

AUTHOR

Zak Seidov, Sep 04 2002

STATUS

approved