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A057468 Numbers n such that 3^n - 2^n is prime. 118
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Some of the larger entries may only correspond to probable primes.

The 1137- and 1352-digit values associated with the terms 2381 and 2833 have been certified prime with Primo. - Rick L. Shepherd, Nov 12 2002

Or, numbers n such that A001047(n) is prime. - Zak Seidov, Sep 17 2006

3^n - 2^n were proved prime for n = 3613, 3853, 3929, 5297, 7417 with Primo. [From David Harrison, Jun 08 2011]

LINKS

Table of n, a(n) for n=1..27.

R. Miles, Synchronization points and associated dynamical invariants

Henri Lifchitz and Renaud Lifchitz, PRP Records.

Primality certificates for 3613 to 7417

MATHEMATICA

Select[Range[10^3], PrimeQ[3^# - 2^#] &] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)

PROG

(PARI) select(p->ispseudoprime(3^n-2^n), primes(100)) \\ Charles R Greathouse IV, Feb 11 2011

CROSSREFS

Cf. A058765, A000043 (Mersenne primes), A001047 (3^n-2^n).

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 2003-2005. 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

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Last modified November 23 22:37 EST 2014. Contains 249866 sequences.