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Search: id:A070179
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| A070179 |
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Primes p such that x^2 = 2 has a solution mod p, but x^(2^2) = 2 has no solution mod p. |
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+0
12
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| 17, 41, 97, 137, 193, 241, 313, 401, 409, 433, 449, 457, 521, 569, 641, 673, 761, 769, 809, 857, 929, 953, 977, 1009, 1129, 1297, 1321, 1361, 1409, 1489, 1657, 1697, 1873, 1993, 2017, 2081, 2137, 2153, 2161, 2297, 2377, 2417, 2521, 2609, 2617, 2633, 2713
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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Primes of the form 8*k + 1 but not x^2 + 64*y^2. - Michael Somos Mar 22 2008
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PROGRAM
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(PARI) forprime(p=2, 2720, x=0; while(x<p&&x^2%p!=2%p, x++); if(x<p, y=0; while(y<p&&y^(2^2)%p!=2%p, y++); if(y==p, print1(p, ", "))))
(PARI) {a(n) = local(m, c, x); if( n<1, 0, c = 0; m = 1; while( c<n, m++; if( isprime(m) & m%8 == 1, x = 0; for(y=1, sqrtint( m \ 64 ), if( issquare( m - 64 * y^2, &x), break)); if( !x, c++ ))); m)} /* Michael Somos Mar 22 2008 */
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CROSSREFS
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Cf. A038873, A040098, A040100, A059667, A070180 - A070188, A014754.
Sequence in context: A087877 A107181 A139879 this_sequence A089637 A139961 A070183
Adjacent sequences: A070176 A070177 A070178 this_sequence A070180 A070181 A070182
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Apr 29 2002
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