

A057468


Numbers k such that 3^k  2^k is prime.


124



2, 3, 5, 17, 29, 31, 53, 59, 101, 277, 647, 1061, 2381, 2833, 3613, 3853, 3929, 5297, 7417, 90217, 122219, 173191, 256199, 336353, 485977, 591827, 1059503
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OFFSET

1,1


COMMENTS

Some of the larger entries may only correspond to probable primes.
The 1137 and 1352digit values associated with the terms 2381 and 2833 have been certified prime with Primo.  Rick L. Shepherd, Nov 12 2002
Or, numbers k such that A001047(k) is prime.  Zak Seidov, Sep 17 2006
3^k  2^k were proved prime for k = 3613, 3853, 3929, 5297, 7417 with Primo.  David Harrison, Jun 08 2011


LINKS

Table of n, a(n) for n=1..27.
Henri Lifchitz and Renaud Lifchitz, PRP Records.
R. Miles, Synchronization points and associated dynamical invariants, Trans. Amer. Math. Soc. 365 (2013), 55035524.
Primality certificates for 3613 to 7417


MATHEMATICA

Select[Prime@ Range@ 941, PrimeQ[3^#  2^#] &] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 and modified by Robert G. Wilson v, Mar 15 2017 *)
ParallelMap[ If[ PrimeQ[3^#  2^#], #, Nothing] &, Prime@ Range@ 941] (* Robert G. Wilson v, Jun 28 2017 *)


PROG

(PARI) select(p>ispseudoprime(3^n2^n), primes(100)) \\ Charles R Greathouse IV, Feb 11 2011


CROSSREFS

Cf. A058765, A000043 (Mersenne primes), A001047 (3^n2^n).
Subset of A000040.
Sequence in context: A215311 A215315 A065725 * A127062 A214735 A216061
Adjacent sequences: A057465 A057466 A057467 * A057469 A057470 A057471


KEYWORD

nonn,hard,nice,more


AUTHOR

Robert G. Wilson v, Sep 09 2000


EXTENSIONS

a(20) = 90217 found by Mike Oakes, Feb 23 2001
Terms a(21) = 122219, a(22) = 173191, a(23) = 256199 were found by Mike Oakes in 20032005. Corresponding numbers of decimal digits are 58314, 82634, 122238.
a(24) = 336353 found by Mike Oakes, Oct 15 2007. It corresponds to a probable prime with 160482 decimal digits.
a(25) = 485977 found by Mike Oakes, Sep 06 2009; it corresponds to a probable prime with 231870 digits.  Mike Oakes, Sep 08 2009
a(26) = 591827 found by Mike Oakes, Aug 25 2009; it corresponds to a probable prime with 282374 digits.
a(27) = 1059503 found by Mike Oakes, Apr 12 2012; it corresponds to a probable prime with 505512 digits.  Mike Oakes, Apr 14 2012


STATUS

approved



