A076481 Primes of the form (3^n-1)/2.

13, 1093, 797161, 3754733257489862401973357979128773, 6957596529882152968992225251835887181478451547013

Offset: 1

Author

Dean Hickerson, Oct 14 2002

Keywords

• nonn

Comments

All primes p whose reciprocals belong to the middle-third Cantor set satisfy an equation of the form 2pK + 1 = 3^n. This sequence is the special case K = 1. See reference. [Christian Salas, Jul 04 2011]

Conjecture: primes p such that sigma(2p+1) = 3*p+1. Sigma(2*a(n)+1) = 3*a(n) +1 holds for all first 9 terms. - Jaroslav Krizek, Sep 28 2014

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..9
• Christian Salas, On prime reciprocals in the Cantor set, arXiv:0906.0465v5 [math.NT], 2009-2011.
• Christian Salas, Cantor primes as prime-valued cyclotomic polynomials, arXiv preprint arXiv:1203.3969 [math.NT], 2012.

Crossrefs

The exponents n are in A028491. Cf. A075081.

Programs

Magma

[a: n in [1..200] | IsPrime(a) where a is (3^n-1) div 2 ]; // Vincenzo Librandi, Dec 09 2011

Maple

A076481:=n->`if`(isprime((3^n-1)/2), (3^n-1)/2, NULL): seq(A076481(n), n=1..100); # Wesley Ivan Hurt, Sep 30 2014

Mathematica

Select[Table[(3^n-1)/2, {n,0,500}], PrimeQ] (* Vincenzo Librandi, Dec 09 2011 *)

PARI

for(n=3,99,if(ispseudoprime(t=3^n\2),print1(t", "))) \\ Charles R Greathouse IV, Jul 02 2013