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A125646
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Smallest odd prime base q such that p^5 divides q^(p-1) - 1, where p = prime(n).
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12
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97, 487, 14557, 32261, 275393, 220861, 15541, 2342959, 1051847, 24639193, 40373093, 70697317, 31851901, 47289133, 456330179, 10000453, 154075723, 130702609, 304154189, 143584109, 183298237, 79451167, 1058782027, 352845203, 567620413, 4592184511, 5890772963, 9651540247, 4081988041, 4772484029
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OFFSET
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1,1
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LINKS
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MAPLE
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f:= proc(n) local p, k, j, q, R;
p:= ithprime(n);
R:= sort(map(rhs@op, [msolve(q^(p-1)-1, p^5)]));
for k from 0 do
for j in R do
q:= k*p^5+j;
if isprime(q) then return q fi;
od
od
end proc:
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MATHEMATICA
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Do[p = Prime[n]; q = 2; While[PowerMod[q, p-1, p^5] != 1, q = NextPrime[q]]; Print[q], {n, 100}] (* Ryan Propper, Mar 31 2007 *)
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PROG
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(PARI) { a(n) = local(p, x, y); if(n==1, return(97)); p=prime(n); x=znprimroot(p^5)^(p^4); vecsort( vector(p-1, i, y=lift(x^i); while(!isprime(y), y+=p^5); y ) )[1] } \\ Max Alekseyev, May 30 2007
(Python)
from itertools import count
from sympy import nthroot_mod, isprime, prime
m = (p:=prime(n))**5
r = sorted(nthroot_mod(1, p-1, m, all_roots=True))
for i in count(0, m):
for a in r:
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CROSSREFS
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Cf. A125609, A125610, A125611, A125612, A125632, A125633, A125634, A125635, A125636, A125637, A125645, A125647, A125648, A125649.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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