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A057468
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Numbers n such that 3^n - 2^n is prime.
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107
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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 (rshepherd2(AT)hotmail.com), Nov 12 2002
Or, numbers n such that A001047(n) is prime. - Zak Seidov (zakseidov(AT)yahoo.com), Sep 17 2006
All terms are prime, since (3^n - 2^a) | (3^an - 2^an). [From Charles R Greathouse IV, Jan 10 2011]
3^n - 2^n were proved prime for n = 3613, 3853, 3929, 5297, 7417 with Primo. [From David Harrison, Jun 08 2011]
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LINKS
| R. MILES, SYNCHRONIZATION POINTS AND ASSOCIATED DYNAMICAL INVARIANTS
Henri & Renaud Lifchitz, PRP Records.
Primality certificates for 3613 to 7417
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MATHEMATICA
| Select[Range[10^3], PrimeQ[3^#-2^# ]&] - Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 29 2008
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PROG
| (PARI) select(vector(10^4, i, i), p->ispseudoprime(3^n-2^n)) \\ Charles R Greathouse IV, Feb 11 2011
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CROSSREFS
| Cf. A058765, A000043 (Mersenne primes), A001047 (3^n-2^n).
Sequence in context: A077499 A127061 A065725 * A127062 A029972 A077498
Adjacent sequences: A057465 A057466 A057467 * A057469 A057470 A057471
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KEYWORD
| nonn,hard,nice,more
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 09 2000
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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) = 591827 found by Mike Oakes, Aug 25 2009; it corresponds to a probable prime with 282374 digits. Mike Oakes (mikeoakes2(AT)aol.com), Aug 31 2009
a(26) = 591827 found by Mike Oakes, Aug 25 2009; it corresponds to a probable prime with 282374 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
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