login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A076481 Primes of the form (3^n-1)/2. 19
13, 1093, 797161, 3754733257489862401973357979128773, 6957596529882152968992225251835887181478451547013 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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]

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

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 *)

PROG

(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

CROSSREFS

The exponents n are in A028491. Cf. A075081.

Sequence in context: A128685 A201118 A262632 * A185834 A264249 A195890

Adjacent sequences:  A076478 A076479 A076480 * A076482 A076483 A076484

KEYWORD

nonn

AUTHOR

Dean Hickerson, Oct 14 2002

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy .

Last modified December 4 17:35 EST 2016. Contains 278755 sequences.