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A160245
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a(n) = index of the n-th prime in A051301 (least prime factor of m!+1)
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0
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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MAPLE
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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;
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Frederick Magata (frederick.magata(AT)web.de), May 05 2009
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EXTENSIONS
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STATUS
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approved
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