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Search: id:A087421
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| 2, 2, 2, 7, 29, 127, 727, 5051, 40343, 362897, 3628811, 39916801, 479001629, 6227020867, 87178291219, 1307674368043, 20922789888023, 355687428096031, 6402373705728037, 121645100408832089, 2432902008176640029
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OFFSET
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0,1
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COMMENT
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n! is prime only when n=2. When n>2, for n!+m to be prime, m must be relatively prime to all the numbers from 2 to n. In particular, if m is between 2 and n, then (n!+m) will be divisible by m. Thus a(n) must be either n!+1, or else larger than n!+n.
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FORMULA
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a(n) = min { p[i] | p[i]>=n! }, where p[i] is the set of prime numbers.
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EXAMPLE
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a(0)=2 since 0!=1 and 2 is the smallest prime >=1. a(4)=29 since 4!=24 and 29 is the smallest prime >=24.
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MATHEMATICA
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NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; Table[ NextPrim[n! - 1], {n, 0, 20}] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 25 2003)
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CROSSREFS
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Cf. A006990, A037151, A000142.
Sequence in context: A023573 A138757 A121258 this_sequence A132697 A137508 A055921
Adjacent sequences: A087418 A087419 A087420 this_sequence A087422 A087423 A087424
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KEYWORD
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nonn
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AUTHOR
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Mitch Cervinka (puritan(AT)planetkc.com), Oct 22 2003
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EXTENSIONS
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Edited, corrected and extended by Robert G. Wilson v (rgwv(AT)rgwv.com) and Ray Chandler (rayjchandler(AT)sbcglobal.net), Oct 25 2003
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