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A125646 Smallest odd prime base q such that p^5 divides q^(p-1) - 1, where p = Prime[n]. +0
12
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 (list; graph; listen)
OFFSET

1,1

LINKS

W. Keller and J. Richstein Fermat quotients that are divisible by p.

MATHEMATICA

Do[p = Prime[n]; q = 2; While[PowerMod[q, p-1, p^5] != 1, q = NextPrime[q]]; Print[q], {n, 100}] - Ryan Propper (rpropper(AT)stanford.edu), Mar 31 2007

PROGRAM

(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 (maxale(AT)gmail.com), May 30 2007

CROSSREFS

Cf. A125609, A125610, A125611, A125612, A125632, A125633, A125634, A125635, A125636, A125637, A125645, A125647, A125648, A125649.

Sequence in context: A107213 A157331 A142834 this_sequence A142574 A142765 A144130

Adjacent sequences: A125643 A125644 A125645 this_sequence A125647 A125648 A125649

KEYWORD

nonn

AUTHOR

Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 29 2006

EXTENSIONS

More terms from Ryan Propper (rpropper(AT)stanford.edu), Mar 31 2007

More terms from Max Alekseyev (maxale(AT)gmail.com), May 30 2007

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Last modified March 20 09:10 EDT 2010. Contains 173642 sequences.


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