

A088250


a(n) is the smallest number k such that r*k + 1 is prime for all r = 1 to n.


11



1, 1, 2, 330, 10830, 25410, 512820, 512820, 12960606120, 434491727670, 1893245380950, 71023095613470, 878232256181280, 11429352906540438870
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OFFSET

1,3


COMMENTS

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]


LINKS

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.


EXAMPLE

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.


MATHEMATICA

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 *)


CROSSREFS

Cf. A088251, A088252, A088651, A125838, A125839.
Sequence in context: A012606 A012729 A173750 * A142355 A203608 A264942
Adjacent sequences: A088247 A088248 A088249 * A088251 A088252 A088253


KEYWORD

nonn,more


AUTHOR

Amarnath Murthy, Sep 26 2003


EXTENSIONS

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


STATUS

approved



