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A088250
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a(n) is the smallest number k such that r*k + 1 is prime for all r = 1 to n.
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11
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1, 1, 2, 330, 10830, 25410, 512820, 512820, 12960606120, 434491727670, 1893245380950, 71023095613470, 878232256181280, 11429352906540438870
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OFFSET
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1,3
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COMMENTS
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Conjectures: (1) Sequence is infinite. (2) For every n there are infinitely many arithmetic progressions with n successive primes.
Both conjectures follow from Dickson's conjecture. [Charles R Greathouse IV, Mar 14 2011]
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LINKS
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Table of n, a(n) for n=1..14.
Carlos Rivera, Puzzle 379. SG primes and its prime average, The Prime Puzzles and Problems Connection.
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EXAMPLE
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a(11) = 1893245380950 because all eleven numbers 1*1893245380950 + 1, 2*1893245380950 + 1, 3*1893245380950 + 1, ..., 10*1893245380950 + 1 & 11*1893245380950 + 1 are prime and 1893245380950 is the smallest number with such property.
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MATHEMATICA
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a[n_] := Block[{k = If[n < 4, 1, 6], s}, s = k; While[! AllTrue[k Range[n] + 1, PrimeQ], k += s]; k]; Array[a, 8] (* Giovanni Resta, Mar 31 2017 *)
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CROSSREFS
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Cf. A088251, A088252, A088651, A125838, A125839.
Sequence in context: A012606 A012729 A173750 * A142355 A203608 A264942
Adjacent sequences: A088247 A088248 A088249 * A088251 A088252 A088253
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KEYWORD
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nonn,more
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AUTHOR
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Amarnath Murthy, Sep 26 2003
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EXTENSIONS
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Edited by Don Reble, Sep 29 2003
Entry revised by N. J. A. Sloane, Jan 05 2007
a(14) from Giovanni Resta, Mar 31 2017
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STATUS
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approved
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