A125839 a(n) is the smallest number m such that k*m - 1 is prime for all k=3,4,...,n.

1, 1, 6, 18, 120, 1260, 1485540, 28667100, 28667100, 842889105240, 2281585556250, 163881570370980, 45187548280664790

Offset: 3

Author

Luke Pebody (luke.pebody(AT)gmail.com), Jan 02 2007

Keywords

• hard
• more
• nonn

Comments

For n > 6, 10 divides a(n).

Examples

			a(11)=28667100 because 3*28667100-1, 4*28667100-1, 5*28667100-1, 6*28667100-1, 7*28667100-1, 8*28667100-1, 9*28667100-1, 10*28667100-1 & 11*28667100-1 are prime and 28667100 is the smallest number with this property.
		

Links

• Carlos Rivera, Problems & puzzles.

Crossrefs

Cf. A125838, A088651, A088250.

Programs

Mathematica

a[n_] := Block[{k = If[n<5, 1, 6], s}, s = k;  While[! AllTrue[k Range[3, n] - 1, PrimeQ], k += s]; k]; a /@ Range[3, 9] (* Giovanni Resta, Mar 29 2017 *)

Extensions

a(12)-a(13) from Farideh Firoozbakht

a(14)-a(15) from Giovanni Resta, Mar 30 2017