|
| |
|
|
A057468
|
|
Numbers n such that 3^n - 2^n is prime.
|
|
114
|
|
|
|
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(vector(10^4, i, i), p->ispseudoprime(3^n-2^n)) \\ 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 (Mikeoakes2(AT)aol.com), 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 6 2009; it corresponds to a probable prime with 231870 digits. Mike Oakes (mikeoakes2(AT)aol.com), 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 (mikeoakes2(AT)aol.com), Apr 14 2012
|
|
|
STATUS
|
approved
|
| |
|
|
