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A125645
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Smallest odd prime base q such that p^4 divides q^(p-1) - 1, where p = prime(n).
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12
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17, 163, 443, 3449, 45989, 239, 15541, 2819, 60793, 78017, 690143, 398023, 1977343, 574081, 1513367, 4388179, 3198427, 8065789, 3246107, 1353383, 5934307, 15631613, 2864371, 14754769, 15012733, 1358891, 32414783, 119551, 21860063, 11281097
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OFFSET
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1,1
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..10000
W. Keller and J. Richstein Fermat quotients that are divisible by p.
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MAPLE
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f:= proc(n) local p, r, S, i, s, t;
uses numtheory;
p:= ithprime(n);
r:= primroot(p^4);
S:= sort([seq(r &^ (i*p^3) mod p^4, i=0..p-2)]);
for i from 0 do
for s in S do
t:= i*p^4+s;
if t::odd and isprime(t) then return t fi
od od
end proc:
f(1):= 1:
map(f, [$1..100]); # Robert Israel, Feb 12 2017
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PROG
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(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
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CROSSREFS
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Cf. A125609, A125610, A125611, A125612, A125632, A125633, A125634, A125635, A125636, A125637, A125646, A125647, A125648, A125649.
Sequence in context: A164746 A198859 A160295 * A068518 A155664 A096192
Adjacent sequences: A125642 A125643 A125644 * A125646 A125647 A125648
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk, Nov 29 2006
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EXTENSIONS
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More terms from Max Alekseyev, May 30 2007
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STATUS
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approved
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