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A103310
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Largest prime primitive root of n that is less than n, or 0 if none exists.
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6
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0, 0, 0, 2, 3, 3, 5, 5, 0, 5, 7, 7, 0, 11, 5, 0, 0, 11, 11, 13, 0, 0, 19, 19, 0, 23, 19, 23, 0, 19, 0, 17, 0, 0, 31, 0, 0, 19, 29, 0, 0, 29, 0, 29, 0, 0, 43, 43, 0, 47, 47, 0, 0, 41, 47, 0, 0, 0, 47, 47, 0, 59, 53, 0, 0, 0, 0, 61, 0, 0, 0, 67, 0, 59, 61, 0, 0, 0, 0, 59, 0, 59, 71, 79, 0, 0, 73
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OFFSET
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0,4
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LINKS
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Robert Israel, 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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hasproot:= proc(n)
if n::odd then nops(numtheory:-factorset(n))=1
else padic:-ordp(n, 2)=1 and nops(numtheory:-factorset(n/2))=1
fi
end proc;
hasproot(2):= true: hasproot(4):= true:
f:= proc(n) local p, t;
if not hasproot(n) then return 0 fi;
t:= numtheory:-phi(n);
p:= prevprime(n);
while not numtheory:-order(p, n)=t do
if p = 2 then return 0 fi;
p:= prevprime(p);
od;
p
end proc:
f(0):= 0: f(1):= 0: f(2):= 0:
map(f, [$0..100]); # Robert Israel, Sep 08 2020
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CROSSREFS
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Cf. A001918, A046144, A046145, A046146, A103309.
Sequence in context: A158745 A175108 A265145 * A046146 A081768 A273493
Adjacent sequences: A103307 A103308 A103309 * A103311 A103312 A103313
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KEYWORD
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easy,nonn
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AUTHOR
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Harry J. Smith, Jan 29 2005
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STATUS
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approved
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