This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A058959 Numbers n such that 3^n - 4 is prime. 26
 2, 3, 5, 21, 31, 37, 41, 53, 73, 101, 175, 203, 225, 455, 557, 651, 1333, 4823, 20367, 32555, 52057, 79371, 267267, 312155 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS From M. F. Hasler and Farideh Firoozbakht, Oct 30 2009: (Start) If Q is a perfect number such that gcd(Q, 3(3^a(n)-4))=1 then m=3^(a(n)-1) (3^a(n)-4)Q is a solution of the equation sigma(x)=3(x+Q). This is a result of the following theorem. Theorem : If for a prime q, Q is a (q-1)-perfect number and p=q^k-q-1 is a prime such that gcd(Q, p*q)=1, then m=p*q^(k-1)*Q is a solution of the equation sigma(x)=q(x+Q). The proof is easy. (End) From M. F. Hasler and Farideh Firoozbakht, Dec 07 2009: (Start) 2 is the only even term of this sequence because if n is an even number greater than 2 then 3^n-4=(3^(n/2)-2)*(3^(n/2)+2) is composite. We have also found the following generalization of this theorem. See comment lines of the sequence A171271. Theorem : If for a prime q, Q is a (q-1)-perfect number and for some integers k and m, p=q^k-m*q-1 is a prime such that gcd(Q, p*q)=1, then x=p*q^(k-1)*Q is a solution of the equation sigma(x)=q(x+m*Q). The proof is easy. (End) 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. MATHEMATICA Do[ If[ PrimeQ[3^n - 4], Print[n] ], {n, 1, 3000} ] PROG (PARI) for(n=1, 10^3, if(ispseudoprime(3^n-4), print1(n, ", "))) \\ Derek Orr, Mar 06 2015 (MAGMA) [n: n in [1..10^3]| IsPrime(3^n-4)]; // Vincenzo Librandi, Mar 24 2015 CROSSREFS Cf. A014224, A171271. - M. F. Hasler and Farideh Firoozbakht, Dec 07 2009 Sequence in context: A291673 A076383 A024766 * A065398 A084838 A051694 Adjacent sequences:  A058956 A058957 A058958 * A058960 A058961 A058962 KEYWORD nonn,more AUTHOR Robert G. Wilson v, Jan 13 2001 EXTENSIONS a(18)=4823, corresponding to a certified prime, from Ryan Propper, Jun 30 2005 a(19)=20367 from Ray Chandler, Jul 25 2011 a(20)=32555, a(21)=52057 from Henri Lifchitz, Jan 2005 a(22)=79371 from Ray Chandler, Jul 25 2011 a(23)=267267 from Roman Ilyukhin, Oct 17 2014 a(24)=312155 from Roman Ilyukhin, Feb 28 2015 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 October 23 19:37 EDT 2019. Contains 328373 sequences. (Running on oeis4.)