The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A051783 Numbers k such that 3^k + 2 is prime. 45
 0, 1, 2, 3, 4, 8, 10, 14, 15, 24, 26, 36, 63, 98, 110, 123, 126, 139, 235, 243, 315, 363, 386, 391, 494, 1131, 1220, 1503, 1858, 4346, 6958, 7203, 10988, 22316, 33508, 43791, 45535, 61840, 95504, 101404, 106143, 107450, 136244, 178428, 361608, 504206 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS From Farideh Firoozbakht and M. F. Hasler, Dec 06 2009: (Start) If Q is a perfect number such that gcd(Q, 3(3^a(n) + 2)) = 1, then x = 3^(a(n) - 1)*(3^a(n) + 2)*Q is a solution of the equation sigma(x) = 3(x - Q). This is a result of the following theorem: Theorem: If Q is a (q-1)-perfect number for some prime q, then for all integers t, the equation sigma(x) = q*x - (2t+1)*Q has the solution x = q^(k-1)*p*Q whenever k is a positive integer such that p = q^k + 2t is prime, gcd(q^(k-1), p) = 1 and gcd(q^(k-1)*p,Q) = 1. Note that by taking t = -1/2(m*q+1), this theorem gives us some solutions of the equation sigma(x) = q *(x + m*Q). See comment lines of the sequence A058959. (End) No further terms < 200000. - Ray Chandler, Jul 31 2011 A090649 implies that 361608 is a member of this sequence. - Robert Price, Aug 18 2014 No further terms < 320000. - Luke W. Richards, Mar 04 2018 a(45) and a(46) are probable primes because a primality certificate has not yet been found. They have been verified PRP with mprime. - Luke W. Richards, May 04 2018 No further terms < 1300000. - Luke W. Richards, May 17 2018 LINKS F. Firoozbakht, M. F. Hasler, Variations on Euclid's formula for Perfect Numbers, JIS 13 (2010) #10.3.1. Henri & Renaud Lifchitz, PRP Records. EXAMPLE 3^8 + 2 = 6563 is prime, so 8 is in the sequence. 3^26 + 2 = 2541865828331, a prime number, so 26 is in the sequence. MATHEMATICA A051783 = Select[Range[0, 20000], PrimeQ[3^# + 2] &] PROG (PARI) is(n)=ispseudoprime(3^n+2) \\ Charles R Greathouse IV, Mar 21 2013 CROSSREFS Cf. A057735, A087885, A014224, A058959. Sequence in context: A135772 A209064 A222264 * A033083 A302406 A328092 Adjacent sequences:  A051780 A051781 A051782 * A051784 A051785 A051786 KEYWORD nonn,hard AUTHOR Jud McCranie, Dec 09 1999 EXTENSIONS {4346, 6958, 7203} from David J. Rusin, Sep 29 2000 10988 from Ray Chandler, Nov 21 2004 {22316, 33508} found by Henri Lifchitz, Sep-Oct 2002 {43791, 45535, 61840} found by Henri Lifchitz, Oct-Nov 2004 95504 found by Wojciech Florek Dec 15 2005. - Alexander Adamchuk, Mar 02 2008 Edited by N. J. A. Sloane, Dec 19 2009 {101404, 106143, 107450, 136244} from Mike Oakes, Nov 2009 178428 from Ray Chandler, Jul 29 2011 a(45)-a(46) from Luke W. Richards, May 04 2018 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 10 00:25 EDT 2020. Contains 335570 sequences. (Running on oeis4.)