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A084727
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Primes arising in A084726.
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2
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2, 3, 7, 281, 76561, 576577, 17873857, 643458817, 337767408001, 21617114112001, 39916801, 119715577952256001, 1980990543353657472001, 26582634158080001, 3577861898239093446857008573440001, 711975497511453268455460274177
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OFFSET
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1,1
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COMMENTS
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Smallest prime of the form: 1 + product of n terms of an arithmetic progression with first term 1.
Conjecture: All terms exist.
If n! + 1 is prime (A002981) then a(n) = A088332(n). - Hugo Pfoertner, Nov 18 2004
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LINKS
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Nathaniel Johnston, Table of n, a(n) for n = 1..100
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FORMULA
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a(n) = 1 + Product_{i = 0..n-1} (1 + i*A084726(n)). - David Wasserman, Jan 03 2005
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EXAMPLE
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a(1) = 2 = 1 + 1;
a(4) = 281 = 1*4*7*10 + 1 (1*2*3*4 + 1 = 25 is composite);
a(5) = 76561 = 1*8*15*22*29 + 1.
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MAPLE
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A084727 := proc(n) local k, p: for k from 1 do p:=1+mul(1+j*k, j=0..n-1): if(isprime(p))then return p: fi: od: end: seq(A084727(n), n=1..16); # Nathaniel Johnston, Jun 26 2011
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MATHEMATICA
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np[n_]:=Module[{k=1}, While[!PrimeQ[Times@@NestList[k+#&, 1, n-1]+1], k++]; Times@@NestList[k+#&, 1, n-1]+1]; Array[np, 20] (* Harvey P. Dale, Aug 05 2021 *)
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CROSSREFS
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Cf. A002981, A084726, A088332.
Sequence in context: A063869 A079637 A062662 * A100763 A132538 A334726
Adjacent sequences: A084724 A084725 A084726 * A084728 A084729 A084730
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 13 2003
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EXTENSIONS
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More terms from David Wasserman, Jan 03 2005
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STATUS
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approved
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