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A034881
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a(1) = 1; for n>1, a(n) = smallest integer > a(n-1) such that a(n)*a(n-i)+1 is prime for all 1 <= i <= n-1.
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4
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1, 2, 6, 18, 30, 270, 606, 123120, 888456, 23070450, 238550160, 8282903640, 72789145650, 15681266370000, 18216437241240
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OFFSET
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1,2
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COMMENTS
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a(n) exists for every n if Dickson's conjecture is true. - Charles R Greathouse IV, Nov 30 2012
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LINKS
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Table of n, a(n) for n=1..15.
Bill Taylor et. al., Sets producing primes, sci.math (2003)
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EXAMPLE
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After a(1)=1, a(2)=2, a(3)=6, we want m, the smallest number >6 such that m+1, 2m+1 and 6m+1 are all prime: this is m = 18 = a(4).
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MATHEMATICA
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f[s_List] := Block[{k = s[[-1]] + 1, m = s}, While[ Union@ PrimeQ[k*m + 1] != {True}, k++]; Append[s, k]]; Nest[f, {1}, 10] (* Robert G. Wilson v, Dec 02 2012 *)
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CROSSREFS
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Cf. A219761, A093483.
Sequence in context: A185382 A066286 A197168 * A146345 A064842 A101695
Adjacent sequences: A034878 A034879 A034880 * A034882 A034883 A034884
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KEYWORD
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nonn
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AUTHOR
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Erich Friedman
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EXTENSIONS
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a(9) to a(13) found by Phil Carmody.
a(14), a(15) from Don Reble (djr(AT)nk.ca), Oct 15 2012; a(16) > 2*10^16.
Edited by N. J. A. Sloane, Dec 01 2012
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STATUS
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approved
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