This site is supported by donations to The OEIS Foundation.



Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A076481 Primes of the form (3^n-1)/2. 22
13, 1093, 797161, 3754733257489862401973357979128773, 6957596529882152968992225251835887181478451547013 (list; graph; refs; listen; history; text; internal format)



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


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]

Christian Salas, Cantor primes as prime-valued cyclotomic polynomials, arXiv preprint arXiv:1203.3969, 2012.


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


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


(MAGMA) [a: n in [1..200] | IsPrime(a) where a is (3^n-1) div 2 ]; // 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


The exponents n are in A028491. Cf. A075081.

Sequence in context: A201118 A282968 A262632 * A185834 A264249 A195890

Adjacent sequences:  A076478 A076479 A076480 * A076482 A076483 A076484




Dean Hickerson, Oct 14 2002



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 12 09:36 EST 2019. Contains 329953 sequences. (Running on oeis4.)