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%I #14 May 03 2021 15:03:10
%S 17,163,443,3449,45989,239,15541,2819,60793,78017,690143,398023,
%T 1977343,574081,1513367,4388179,3198427,8065789,3246107,1353383,
%U 5934307,15631613,2864371,14754769,15012733,1358891,32414783,119551,21860063,11281097
%N Smallest odd prime base q such that p^4 divides q^(p-1) - 1, where p = prime(n).
%H Robert Israel, <a href="/A125645/b125645.txt">Table of n, a(n) for n = 1..10000</a>
%H W. Keller and J. Richstein <a href="http://www1.uni-hamburg.de/RRZ/W.Keller/FermatQuotient.html">Fermat quotients that are divisible by p</a>.
%p f:= proc(n) local p, r, S,i,s,t;
%p uses numtheory;
%p p:= ithprime(n);
%p r:= primroot(p^4);
%p S:= sort([seq(r &^ (i*p^3) mod p^4, i=0..p-2)]);
%p for i from 0 do
%p for s in S do
%p t:= i*p^4+s;
%p if t::odd and isprime(t) then return t fi
%p od od
%p end proc:
%p f(1):= 1:
%p map(f, [$1..100]); # _Robert Israel_, Feb 12 2017
%o (PARI) { a(n) = local(p,x,y); if(n==1,return(17)); p=prime(n); x=znprimroot(p^4)^(p^3); vecsort( vector(p-1,i, y=lift(x^i);while(!isprime(y),y+=p^4);y ) )[1] } - _Max Alekseyev_, May 30 2007
%Y Cf. A125609, A125610, A125611, A125612, A125632, A125633, A125634, A125635, A125636, A125637, A125646, A125647, A125648, A125649.
%K nonn
%O 1,1
%A _Alexander Adamchuk_, Nov 29 2006
%E More terms from _Max Alekseyev_, May 30 2007
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