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Search: id:A083521
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| A083521 |
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Smallest prime that is the product of n consecutive integers + 1, or 0 if no such number exists. |
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+0
3
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| 2, 3, 7, 0, 2521, 20161, 604801, 6652801, 726485761, 39916801, 39916801, 140792940288001, 14820309504001, 10461394944001, 641171050071552001, 425757851430912001, 9366672731480064001, 8515157028618240001
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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The product of four consecutive integers + 1 is always composite (a square), so a(4) = 0. Are there any more zeros in the sequence?
The Pocklington-Lehmer "P-1" primality test is used, as implemented in PARI 2.1.3.
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EXAMPLE
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1*2*3*4*5 + 1 = 121 = 11*11 and 2*3*4*5*6 + 1 = 721 = 7*103 are composite, but 3*4*5*6*7 + 1 = 2521 is prime, so a(5) = 2521.
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PROGRAM
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(PARI) m=1000; for(n=1, 18, b=0; k=1; while(b<1&&k<m, if(!isprime(p=prod(j=k, k+n-1, j)+1, 1), k++, b=1)); print1(if(k<m, p, 0), ", "))
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CROSSREFS
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Cf. A083520, A083522.
Sequence in context: A015766 A117024 A023048 this_sequence A104691 A011160 A068960
Adjacent sequences: A083518 A083519 A083520 this_sequence A083522 A083523 A083524
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy and Meenakshi Srikanth (amarnath_murthy(AT)yahoo.com), May 05 2003
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EXTENSIONS
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Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de) and Don Reble (djr(AT)nk.ca), May 06 2003
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