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Search: id:A087564
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| A087564 |
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a(n) = smallest prime of the form n*(n+1)*(n+2)...(n+k) + 1, or 0 if no such prime exists. |
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+0
4
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| 2, 3, 13, 5, 31, 7, 55441, 73, 991, 11, 670442572801, 13, 2731, 211, 241, 17, 307, 19, 4037881, 421, 463, 23, 725902806896876799590400001, 601, 17551, 530122321, 757, 29, 45143585625601, 31, 5296855682339020801, 63606090241, 1123, 42841
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(n) = n+1 iff n+1 is prime. Conjecture: No term is zero.
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EXAMPLE
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7+1 = 8, 7*8+1 = 57, 7*8*9+1 = 505, 7*8*9*10+1 = 5041 are all composite, but 7*8*9*10*11 + 1 = 55441 is prime, so a(7) = 55441.
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MAPLE
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for n from 1 to 70 do k := 0: while(not isprime(1+product(n+i, i=0..k ))) do k := k+1:od:a[n] := 1+product(n+i, i=0..k):od:seq(a[l], l=1..70); (from Sascha Kurz)
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PROGRAM
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(PARI) for(n=1, 34, k=0; m=n; while(!isprime(m+1, 1), k++; m=m*(n+k)); print1(m+1, ", "))
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CROSSREFS
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Cf. A087565.
Sequence in context: A076988 A128369 A087568 this_sequence A057776 A110362 A074478
Adjacent sequences: A087561 A087562 A087563 this_sequence A087565 A087566 A087567
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 15 2003
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EXTENSIONS
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Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de) and Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Sep 20 2003
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