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Smallest n-Knödel number, i.e., smallest composite c > n such that each b < c coprime to c satisfies b^(c-n) == 1 (mod c).
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%I #10 Apr 07 2016 02:36:55

%S 561,4,9,6,25,8,15,12,21,12,15,16,33,24,21,20,65,24,51,24,45,24,33,32,

%T 69,30,39,40,65,36,87,40,45,44,51,40,85,56,57,48,65,72,91,48,63,66,69,

%U 60,141,56,63,60,65,72,75,60,63,70,87,72,133,122,93,80,165

%N Smallest n-Knödel number, i.e., smallest composite c > n such that each b < c coprime to c satisfies b^(c-n) == 1 (mod c).

%H Felix Fröhlich, <a href="/A265261/b265261.txt">Table of n, a(n) for n = 1..4000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Knödel_number">Knödel number</a>.

%t Table[SelectFirst[Range[n + 1, 10^3], Function[c, CompositeQ@ c && AllTrue[Range[1, c - 1] /. x_ /; ! CoprimeQ[x, c] -> Nothing, Mod[#^(c - n), c] == 1 &]]], {n, 65}] (* _Michael De Vlieger_, Apr 06 2016, Version 10 *)

%o (PARI) a(n) = forcomposite(c=n+1, , my(i=0, j=0); for(b=1, c-1, if(gcd(b, c)==1, i++; if(Mod(b, c)^(c-n)==1, j++))); if(i==j, return(c)))

%Y Cf. A050990, A033553, A050992, A050993, A208154, A208155, A208156, A208157, A208158.

%K nonn

%O 1,1

%A _Felix Fröhlich_, Apr 06 2016