

A002253


Numbers n such that 3*2^n+1 is prime.
(Formerly M1318 N0506)


20



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
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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. AddisonWesley, 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. 381384.
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

Table of n, a(n) for n=1..49.
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
Y. Gallot, Proth.exe: Windows Program for Finding Large Primes
S. W. Golomb, Properties of the sequence 3.2^n+1, Math. Comp., 30 (1976), 657663.
S. W. Golomb, Properties of the sequence 3.2^n+1, Math. Comp., 30 (1976), 657663. [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), 673681. [Annotated scanned copy of selected pages. The first page is (accidentally) included with the scan of the Wilson letter below.]
R. G. Wilson v, Letter (FAX) to N. J. A. Sloane, May 20 1994, concerning A002253A002274, A000043, A002235A002240, A001770A001775, A007117, and many other sequences
Eric Weisstein's World of Mathematics, Proth Prime
R. G. Wilson, V, Letter to N. J. A. Sloane, Jan. 1989
Index entries for sequences of n such that k*2^n1 (or k*2^n+1) is prime


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

N. J. A. Sloane


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



