A134753 Numbers k such that 3^(2*k-1) + 2 is prime.

1, 2, 8, 32, 62, 70, 118, 122, 158, 182, 196, 566, 752, 3602, 21896, 22768, 53072

Offset: 1

Author

N. J. A. Sloane, Jan 28 2008

Keywords

• nonn
• more
• hard

Comments

From Enrique Pérez Herrero, Jul 29 2010: (Start)

With: f(n)=3^(2n-1)+2, the non-primality of f(n) is settled when:

if 2 does not divide n, 5 divides f(n) (n>1)

if 3 divides n, 7 divides f(n)

if 5 divides n-4, 11 divides f(n)

if 14 divides n-2, 29 divides f(n)

if 15 divides n-5, 31 divides f(n). (End)

References

• Luis H. Gallardo, Posting to the Number Theory List, Jan 14 2008

Links

• L. H. Gallardo, On a remark of Makowski about perfect numbers, El. Mathem. 65 (3) (2010) 121-126
• Henri & Renaud Lifchitz, PRP Records.

Crossrefs

Cf. A051783, A134752.

Programs

Mathematica

MaxVal = 1000;
dataA134753=Select[Select[Range[MaxVal],#<3||Mod[#,2]==0&&Mod[#,3]!=0&&Mod[#,5]!=4&&Mod[#,14]!=2&&Mod[#,15]!=5&],PrimeQ[3^(2*#-1)+2]&]
A134753[n_Integer] := dataA134753[[n]] /; (n > 0 && n <= Length[dataA134753]) (* Enrique Pérez Herrero, Jul 29 2010 *)

PARI

is(n)=isprime(3^(2*n-1)+2) \\ Charles R Greathouse IV, Jun 06 2017

Formula

({odd terms in A051783} + 1)/2.

Extensions

Typo in prime search corrected Enrique Pérez Herrero, Jul 31 2010

a(15)-a(17) from A051783 by Ray Chandler, Aug 06 2011