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A085427
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Least k such that k*2^n - 1 is prime.
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8
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3, 2, 1, 1, 2, 1, 2, 1, 5, 7, 5, 3, 2, 1, 5, 4, 2, 1, 2, 1, 14, 7, 26, 13, 39, 22, 11, 16, 8, 4, 2, 1, 5, 6, 3, 24, 12, 6, 3, 25, 24, 12, 6, 3, 14, 7, 20, 10, 5, 19, 11, 21, 20, 10, 5, 3, 32, 16, 8, 4, 2, 1, 12, 6, 3, 67, 63, 43, 63, 40, 20, 10, 5, 15, 12, 6, 3, 55, 47, 30, 15, 30, 15, 64, 32, 16, 8
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| First few values of n and k such that k > n are: 1:2, 22:26, 24:39, 65:67, 110:150, 112:140, 135:150, 137:169, ... Also, for n=398 there is an interesting anomaly since k=893 which is > 2n.
Conjecture: for every n there exists a number k < 3n such that k*2^n - 1 is prime. Comment from T. D. Noe: this fails at n=624, where a(n)=2163.
Define sumk=sum from n=1 to N of k(n) Define sumn=sum from n=1 to N of n As N increases the ratio sumk/sumn tends to log(2)/2 = 0.3465735....... so in average k(n) is about 0.35*n and seems to be always < 3.82*n or 11*log(2)/2 [From Pierre CAMI (pierre-cami(AT)bbox.fr), Feb 27 2009]
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LINKS
| Pierre CAMI, Table of n, a(n) for n=0..3000
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MATHEMATICA
| k2np[n_]:=Module[{k=1, x=2^n}, While[!PrimeQ[k x-1], k++]; k]; Array[ k2np, 90, 0] (* From Harvey P. Dale, Nov 19 2011 *)
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CROSSREFS
| Cf. A035050.
Cf. A057778, A126717
Sequence in context: A140736 A140056 A083663 * A172130 A202449 A083716
Adjacent sequences: A085424 A085425 A085426 * A085428 A085429 A085430
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KEYWORD
| easy,nonn
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AUTHOR
| Jason Earls (zevi_35711(AT)yahoo.com), Aug 13 2003
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