login
A088250
a(n) is the smallest number k such that r*k + 1 is prime for all r = 1 to n.
12
1, 1, 2, 330, 10830, 25410, 512820, 512820, 12960606120, 434491727670, 1893245380950, 71023095613470, 878232256181280, 11429352906540438870
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
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
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