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A057468 Numbers n such that 3^n - 2^n is prime. +0
105
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; listen)
OFFSET

1,1

COMMENT

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

3 more terms found by Mike Oakes during 2003 - 2005: a(21) = 122219, a(22) = 173191, a(23) = 256199. Corresponding numbers of decimal digits are 58314, 82634, 122238. - Alexander Adamchuk (alex(AT)kolmogorov.com), Dec 02 2006

All the terms found so far are prime. [From Dmitry Kamenetsky (dkamen(AT)rsise.anu.edu.au), Dec 18 2008]

REFERENCES

Mike Oakes (Mikeoakes2(AT)aol.com), personal communication, Feb 23, 2001, found 90217.

LINKS

Henri & Renaud Lifchitz, PRP Records.

MATHEMATICA

Select[Range[10^3], PrimeQ[3^#-2^# ]&] - Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 29 2008

CROSSREFS

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

Adjacent sequences: A057465 A057466 A057467 this_sequence A057469 A057470 A057471

Sequence in context: A077499 A127061 A065725 this_sequence A127062 A029972 A077498

KEYWORD

nonn,hard,nice

AUTHOR

Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 09 2000

EXTENSIONS

a(24) = 336353 found by Mike Oakes, Oct 15 2007. It corresponds to a probable prime with 160482 decimal digits. - Alexander Adamchuk (alex(AT)kolmogorov.com), Dec 25 2007

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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Last modified November 8 20:39 EST 2009. Contains 166234 sequences.


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