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A023049
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Smallest prime > n having primitive root n, or 0 if no such prime exists.
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2
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2, 3, 5, 0, 7, 11, 11, 11, 0, 17, 13, 17, 19, 17, 19, 0, 23, 29, 23, 23, 23, 31, 47, 31, 0, 29, 29, 41, 41, 41, 47, 37, 43, 41, 37, 0, 59, 47, 47, 47, 47, 59, 47, 47, 47, 67, 59, 53, 0, 53, 53, 59, 71, 59, 59, 59, 67, 73, 61, 73, 67, 71, 67, 0, 71, 79, 71, 71, 71, 79, 83, 83, 83, 79
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OFFSET
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1,1
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COMMENTS
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Indices of record values of a(n)-n are (1, 2, 3, 6, 10, 18, 23, 78, 102, 105, 488, 652, 925, ...). Record values of a(n)/n are 3/2, 5/3, 11/6, 47/23, ... (Is there another n with a(n) > 2n ?) - M. F. Hasler, Feb 21 2017
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = 0 iff n is a square > 1. - M. F. Hasler, Feb 21 2017
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MAPLE
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f:= proc(n) local p;
if issqr(n) then return 0 fi;
p:= nextprime(n);
do
if numtheory:-order(n, p) = p-1 then return p fi;
p:= nextprime(p);
od
end proc:
f(1):= 2:
map(f, [$1..100]); # Robert Israel, Feb 21 2017
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MATHEMATICA
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a[n_] := For[p = 2, p <= 2 n + 1, p = NextPrime[p], If[MemberQ[ PrimitiveRootList[p], n], Return[p]]] /. Null -> 0; Array[a, 100] (* Jean-François Alcover, Mar 05 2019 *)
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PROG
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(PARI) A023049(n)={issquare(n)||forprime(p=n+1, , znorder(Mod(n, p))==p-1&&return(p)); (n==1)*2} \\ M. F. Hasler, Feb 21 2017
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CROSSREFS
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See also A056619, where the primitive root may be larger than the prime, whereas in A023049 it may not be.
Sequence in context: A079344 A096535 A126047 * A240979 A171034 A062007
Adjacent sequences: A023046 A023047 A023048 * A023050 A023051 A023052
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson
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STATUS
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approved
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