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Search: id:A071710
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| A071710 |
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Highly Wilsonian primes: smallest primes p such that w(p)=n where w(n) denote the number of nonnegative integers k such that k! = +1 or -1 (mod n). |
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+0
1
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| 2, 3, 5, 7, 17, 67, 137, 23, 61, 71, 401, 1907, 661, 12227, 29873, 96731, 99721, 154243, 480209, 3408707, 1738901, 27341387
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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Obviously w(n) is at least 2 because 0! = 1! = +1 (mod n) for every n. Also, if p is a prime, then w(p) is at least 4 because (p-2)! = +1 and (p-1)! = -1 (mod p) by Wilson's Theorem. a(22)=1738901 but a(21) is still unknown.
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LINKS
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K. S. Brown, Highly Wilsonian Primes
Charles R Greathouse IV, Home Page [Listed in lieu of email address]
Igor Naverniouk, C++ program
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MATHEMATICA
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w[n_] := Block[{c = k = m = 1}, While[k < n, m = Mod[m *= k, n]; If[m == 1 || m + 1 == n, c++ ]; k++ ]; c]
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PROGRAM
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(PARI) wilsonian(p)={ local(s, t, pMinusOne); pMinusOne=p-1; s=4; t=24; for(k=5, p-3, t=(t*k)%p; if(t==1 || t==pMinusOne, s=s+1) ); s } -Charles R Greathouse IV Jan 24 2007
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CROSSREFS
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Adjacent sequences: A071707 A071708 A071709 this_sequence A071711 A071712 A071713
Sequence in context: A040149 A034970 A048417 this_sequence A048403 A000519 A129693
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KEYWORD
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hard,more,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 03 2002
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EXTENSIONS
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2 more terms from Charles R Greathouse IV Jan 24 2007
27341387 from Igor Naverniouk (igor(AT)cs.utoronto.ca), May 09 2007
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