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A014046
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Second coordinate of fundamental unit of real quadratic field with discriminant A003658(n), n >= 2.
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4
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1, 1, 1, 1, 2, 1, 2, 3, 1, 8, 2, 1, 10, 3, 1, 4, 40, 1, 5, 2, 3, 250, 39, 1, 1, 42, 106, 5, 3, 1138, 2, 1, 8, 25, 146, 2, 273, 2968, 15, 6, 298, 1, 16, 2, 5, 6, 4, 17, 1856, 1, 2, 531, 1, 9384, 97, 3588, 10, 7, 253970, 2, 72664, 7, 3, 6440, 5, 521904, 12, 1, 1, 13
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OFFSET
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2,5
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COMMENTS
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REFERENCES
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H. Cohen, A Course in Computational Algebraic Number Theory, Springer, 1993, pp. 515-519.
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LINKS
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PROG
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(PARI) lista(nn) = { for (n=2, nn, if (isfundamental(n), nc = core(n); m = Mod (nc, 4); if ((m == 2) || (m == 3), d = 1); if ((m == 1), d = 4); b = 1; a = 0; while (a == 0, v = nc*b^2; if (issquare(v-d), a = sqrtint(v-d), if (issquare(v+d), a = sqrtint(v+d))); if (a == 0, b++; ); ); print1(b, ", "); ); ); } \\ Michel Marcus, Sep 25 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Eric Rains (rains(AT)caltech.edu)
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EXTENSIONS
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STATUS
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approved
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