A088250 a(n) is the smallest number k such that r*k + 1 is prime for all r = 1 to n.

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

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