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A046145
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Smallest primitive root modulo n, or 0 if no root exists.
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16
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0, 0, 1, 2, 3, 2, 5, 3, 0, 2, 3, 2, 0, 2, 3, 0, 0, 3, 5, 2, 0, 0, 7, 5, 0, 2, 7, 2, 0, 2, 0, 3, 0, 0, 3, 0, 0, 2, 3, 0, 0, 6, 0, 3, 0, 0, 5, 5, 0, 3, 3, 0, 0, 2, 5, 0, 0, 0, 3, 2, 0, 2, 3, 0, 0, 0, 0, 2, 0, 0, 0, 7, 0, 5, 5, 0, 0, 0, 0, 3, 0, 2, 7, 2, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 5, 0, 0, 5, 3, 0, 0
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OFFSET
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0,4
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COMMENTS
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The value 0 at index 0 says 0 has no primitive roots, but the 0 at index 1 says 1 has a primitive root of 0, the only real 0 in the sequence.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..10000
Eric Weisstein's World of Mathematics, Primitive Root.
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MAPLE
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Contribution from R. J. Mathar, Jul 08 2010: (Start)
A046145 := proc(n) if n <=1 then 0; else pr := numtheory[primroot](n) ; if pr = FAIL then return 0 ; else return pr ; end if; end if; end proc:
seq(A046145(n), n=0..110) ; (End)
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MATHEMATICA
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smallestPrimitiveRoot[n_ /; n <= 1] = 0; smallestPrimitiveRoot[n_] := Block[{pr = PrimitiveRoot[n], g}, If[! NumericQ[pr], g = 0, g = 1; While[g <= pr, If[ CoprimeQ[g, n] && MultiplicativeOrder[g, n] == EulerPhi[n], Break[]]; g++]]; g]; smallestPrimitiveRoot /@ Range[0, 100] (* From Jean-François Alcover, Feb 15 2012 *)
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PROG
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(PARI) for(i=0, 100, p=0; for(q=1, i-1, if(gcd(q, i)==1&&znorder(Mod(q, i))==eulerphi(i), p=q; break)); print1(p", ")) /* V. Raman, Nov 22 2012 */
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CROSSREFS
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Cf. A001918, A046144, A046146, A002233, A071894, A219027, A008330, A010554.
Sequence in context: A118176 A005731 A132962 * A103309 A174621 A007967
Adjacent sequences: A046142 A046143 A046144 * A046146 A046147 A046148
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Eric W. Weisstein
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EXTENSIONS
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Initial terms corrected by Harry J. Smith, Jan 27 2005
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STATUS
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approved
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