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%I #16 Feb 01 2023 12:27:07
%S 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,
%T 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,
%U 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
%N Largest prime primitive root of n that is less than n, or 0 if none exists.
%H Robert Israel, <a href="/A103310/b103310.txt">Table of n, a(n) for n = 0..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimitiveRoot.html">Primitive Root</a>.
%p hasproot:= proc(n)
%p if n::odd then nops(numtheory:-factorset(n))=1
%p else padic:-ordp(n,2)=1 and nops(numtheory:-factorset(n/2))=1
%p fi
%p end proc;
%p hasproot(2):= true: hasproot(4):= true:
%p f:= proc(n) local p,t;
%p if not hasproot(n) then return 0 fi;
%p t:= numtheory:-phi(n);
%p p:= prevprime(n);
%p while not numtheory:-order(p,n)=t do
%p if p = 2 then return 0 fi;
%p p:= prevprime(p);
%p od;
%p p
%p end proc:
%p f(0):= 0: f(1):= 0: f(2):= 0:
%p map(f, [$0..100]); # _Robert Israel_, Sep 08 2020
%t a[n_] := Module[{R = PrimitiveRootList[n], s}, s = Select[R, # < n && PrimeQ[#]&]; If[s == {}, 0, s[[-1]]]];
%t Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Feb 01 2023 *)
%Y Cf. A001918, A046144, A046145, A046146, A103309.
%K easy,nonn
%O 0,4
%A _Harry J. Smith_, Jan 29 2005
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