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A103785
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Primes of the form A019565(2^n-1-k)+A019565(k) with minimum k.
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3
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3, 7, 31, 211, 2311, 15017, 85091, 1616621, 22309297, 3234846617, 200560490131, 3710369067407, 20283350901829, 872184088778017, 307444891294245707, 775932344695001107, 961380175077106319537, 19548063559901161830551
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| This sequence can also be defined as: The Primes of the form primorial P(n)/A019565(k)+A019565(k) with minimum k. Conjecture: sequence is defined for any n>=1.
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EXAMPLE
| for n=1, A019565(2^1-1-0)+A019565(0)=2+1=3 is prime, so a(1)=3;
for n=6, A019565(2^6-1-1)+A019565(1)=15015+2=15017 is prime, so a(6)=15017;
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MATHEMATICA
| nmax = 2^2048; npd = 1; n = 1; npd = npd*Prime[n]; While[npd < nmax, tn = 0; tt = 1; cp = npd/tt + tt; While[(IntegerQ[cp]) && (! (PrimeQ[cp])), tn = tn + 1; tt = 1; k1 = tn; o = 1; While[k1 > 0, k2 = Mod[k1, 2]; If[k2 == 1, tt = tt*Prime[o]]; k1 = (k1 - k2)/2; o = o + 1]; cp = npd/tt + tt]; Print[cp]; n = n + 1; npd = npd*Prime[n]]
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CROSSREFS
| Cf. A019565, A002110.
Sequence in context: A123332 A051342 A002585 * A083772 A093441 A087864
Adjacent sequences: A103782 A103783 A103784 * A103786 A103787 A103788
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KEYWORD
| base,nonn
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AUTHOR
| Lei Zhou (lzhou5(AT)emory.edu), Feb 15 2005
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