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Search: id:A103515
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| A103515 |
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Primes of the form primorial P(k)*2^n-1 with minimal n, n>=0, k>=2. |
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+0
4
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| 5, 29, 419, 2309, 30029, 1021019, 19399379, 892371479, 51757545839, 821495767572479, 14841476269619, 304250263527209, 54873078184468933509119, 2459559130353965639, 521426535635040715679, 15751252788463309939261439
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Conjecture: sequence is defined for all k>=2
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EXAMPLE
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P(2)*2^0-1=3*2-1=5 is prime, so a(2)=5;
P(4)*2^1-1=7*5*3*2*2-1=419 is prime, so a(4)=419;
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MATHEMATICA
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nmax = 2^2048; npd = 2; n = 2; npd = npd*Prime[n]; While[npd < nmax, tt = 1; cp = npd*tt - 1; While[ ! (PrimeQ[cp]), tt = tt*2; cp = npd*tt - 1]; Print[cp]; n = n + 1; npd = npd*Prime[n]]
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CROSSREFS
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Cf. A002110, A005234, A014545, A018239, A006794, A057704, A057705, A103153, A103154.
Adjacent sequences: A103512 A103513 A103514 this_sequence A103516 A103517 A103518
Sequence in context: A020531 A087899 A103783 this_sequence A069142 A072880 A112959
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KEYWORD
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nonn
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AUTHOR
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Lei Zhou (lzhou5(AT)emory.edu), Feb 15 2005
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