A270780 Let p_i = the i-th prime. a(i) is the smallest n>1 such that p_i divides n!-1.

3, 5, 9, 11, 5, 17, 4, 10, 15, 35, 39, 41, 45, 15, 18, 42, 48, 35, 17, 77, 41, 21, 43, 99, 96, 53, 22, 111, 125, 129, 120, 69, 25, 75, 155, 161, 83, 171, 177, 179, 189, 90, 195, 81, 105, 111, 82, 227, 101, 28, 239, 125, 255, 261, 267, 135, 236, 279, 141, 291

Offset: 3

Author

Peter Shor, Mar 22 2016

Keywords

• nonn
• look

Comments

Since p divides (p-2)!-1, the i-th term a(i) cannot be much larger than i log i.

Examples

			For i=3, the third prime is 5, and 5 divides 3!-1.
The 7th prime is 17, and 17 divides 5!-1, so a(7)=5.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..5000

Crossrefs

Cf. A000040, A002982, A270838.

Programs

Maple

a:= proc(n) local k, p; p:=ithprime(n);
      for k from 2 do if irem(k!, p)=1 then return k fi od
    end:
seq(a(n), n=3..100);  # Alois P. Heinz, Mar 23 2016

Mathematica

snpd[p_]:=Module[{n=2},While[!Divisible[n!-1,p],n++];n]; Table[snpd[p],{p,Prime[Range[3,70]]}] (* Harvey P. Dale, Jun 06 2017 *)

Extensions

More terms from Alois P. Heinz, Mar 23 2016