A160245 a(n) = index of the n-th prime in A051301 (least prime factor of m!+1).

2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 3, 2, 2, 6, 1, 3, 3, 1, 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 4, 1, 2, 1, 1, 3, 3, 2, 2, 3, 1, 1, 1, 5, 3, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 4, 2, 2, 5, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 3, 3, 3, 1, 2, 1, 3, 1, 1, 2, 1, 1, 2, 4, 2, 4

Offset: 1

Author

Frederick Magata (frederick.magata(AT)web.de), May 05 2009

Keywords

• nonn

Comments

Because of Wilson's theorem A051301(p-1)=p for every prime p. Hence a(n)>0, and since A051301(k)>k, a(n) is actually finite.

The first 18 values of the sequence were calculated with Maple. The others were derived from T. D. Noe's b-file for b051301.txt.

Examples

			a(17)=3 because A051301(15)=A051301(43)=A051301(58)=59, and there are no other occurrences of 59=17th prime number in A051301.
		

Crossrefs

Cf. A051301, A115092.

Programs

Maple

a:=proc(n) option remember; local k,l,p: p:=ithprime(n): l:=0: for k from 0 to p-2 do if A051301(k)=p then l:=l+1; fi; od; l+1; end;

Mathematica

prev={}; Table[p=Prime[n]; s=Select[Complement[Range[0,p-1],prev], Mod[ #!+1,p]==0&]; prev=Union[s,prev]; Length[s], {n,100}] (* T. D. Noe, May 12 2009 *)

Extensions

Extended by T. D. Noe, May 12 2009