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A172133
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Smallest k such that n(n+1)(n+2)...(n+k-1)+1 is prime.
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2
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1, 1, 2, 1, 2, 1, 5, 2, 3, 1, 10, 1, 3, 2, 2, 1, 2, 1, 5, 2, 2, 1, 18, 2, 3, 6, 2, 1, 9, 1, 12, 7, 2, 3, 8, 1, 74, 2, 5, 1, 2, 1, 14, 3, 6, 1, 9, 18, 3, 2, 3, 1, 3, 2, 19, 3, 2, 1, 2, 1, 3, 2, 115, 5, 6, 1, 16, 5, 2, 1, 2, 1, 5, 3, 2, 3, 2, 1, 6, 2, 6, 1, 3, 3, 10, 3, 5, 1, 2, 2, 3, 24, 8, 3, 13, 1, 13, 3, 2
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OFFSET
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1,3
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LINKS
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FORMULA
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EXAMPLE
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a(2)=1 because 2+1=3 is a prime. a(3)=2 because 3+1=4 is not a prime, but 3*4+1=13 is a prime. a(9)=3 because neither 9+1=10 nor 9*10+1=91=13*7 is a prime, but 9*10*11+1=991 is.
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MATHEMATICA
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a[n_] := Block[{}, For[s = n; k = 1, ! PrimeQ[s + 1], s *= n + k; k++ ]; k] Table[a[n], {n, 1, 100}]
(* Second program *)
Table[k = 1; While[! PrimeQ[1 + Pochhammer[n, k]], k++]; k, {n, 99}] (* Michael De Vlieger, Dec 17 2016 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Cheng Zhang (cz1(AT)rice.edu), Jan 26 2010
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STATUS
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approved
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