This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A002253 Numbers n such that 3*2^n+1 is prime. (Formerly M1318 N0506) 18
 1, 2, 5, 6, 8, 12, 18, 30, 36, 41, 66, 189, 201, 209, 276, 353, 408, 438, 534, 2208, 2816, 3168, 3189, 3912, 20909, 34350, 42294, 42665, 44685, 48150, 54792, 55182, 59973, 80190, 157169, 213321, 303093, 362765, 382449, 709968, 801978, 916773, 1832496, 2145353, 2291610, 2478785, 5082306, 7033641, 10829346 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS From Zak Seidov, Mar 08 2009: (Start) List is complete up to 3941000 according to the list of RB & WK. So far there are only 4 primes: 2, 5, 41, 353. (End) REFERENCES D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 2, p. 614. H. Riesel, ``Prime numbers and computer methods for factorization,'' Progress in Mathematics, Vol. 57, Birkhauser, Boston, 1985, Chap. 4, see pp. 381-384. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Ray Ballinger, Proth Search Page Ray Ballinger and Wilfrid Keller, List of primes k.2^n + 1 for k < 300 C. K. Caldwell, The Prime Pages S. W. Golomb, Properties of the sequence 3.2^n+1, Math. Comp., 30 (1976), 657-663. S. W. Golomb, Properties of the sequence 3.2^n+1, Math. Comp., 30 (1976), 657-663. [Annotated scanned copy] Wilfrid Keller, List of primes k.2^n - 1 for k < 300 R. M. Robinson, A report on primes of the form k.2^n+1 and on factors of Fermat numbers, Proc. Amer. Math. Soc., 9 (1958), 673-681. [Annotated scanned copy of selected pages. The first page is (accidentally) included with the scan of the Wilson letter below.] Eric Weisstein's World of Mathematics, Proth Prime R. G. Wilson, V, Letter to N. J. A. Sloane, Jan. 1989 PROG (PARI) is(n)=isprime(3*2^n+1) \\ Charles R Greathouse IV, Feb 17 2017 CROSSREFS Cf. A002254, A004119, A181565. See A039687 for the actual primes. Sequence in context: A243680 A280381 A105107 * A032716 A132229 A028750 Adjacent sequences:  A002250 A002251 A002252 * A002254 A002255 A002256 KEYWORD hard,nonn AUTHOR EXTENSIONS Corrected and extended according to the list of Ray Ballinger and Wilfrid Keller by Zak Seidov, Mar 08 2009 Edited by N. J. A. Sloane, Mar 13 2009 Two more terms (from http://web.archive.org/web/20161028080239/http://www.prothsearch.net/riesel.html), Joerg Arndt, Apr 07 2013 One more term (from http://primes.utm.edu/primes/page.php?id=116922), Fabrice Le Foulher, Mar 09 2014 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.