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%I #5 Mar 14 2023 03:40:02
%S 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,
%T 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,
%U 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
%N a(n) = index of the n-th prime in A051301 (least prime factor of m!+1)
%C 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.
%C 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.
%e a(17)=3 because A051301(15)=A051301(43)=A051301(58)=59, and there are no other occurrences of 59=17th prime number in A051301.
%p 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;
%t 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 *)
%Y Cf. A051301, A115092.
%K nonn
%O 1,1
%A Frederick Magata (frederick.magata(AT)web.de), May 05 2009
%E Extended by _T. D. Noe_, May 12 2009
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