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Search: id:A160098
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| A160098 |
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Positive numbers y such that y^2 is of the form x^2+(x+601)^2 with integer x. |
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4
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| 425, 601, 1261, 1289, 3005, 7141, 7309, 17429, 41585, 42565, 101569, 242369, 248081, 591985, 1412629, 1445921, 3450341, 8233405, 8427445, 20110061, 47987801, 49118749, 117210025, 279693401, 286285049, 683150089, 1630172605
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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(-297, a(1)) and (A111258(n), a(n+1)) are solutions (x, y) to the Diophantine equation x^2+(x+601)^2 = y^2.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (843+418*sqrt(2))/601 for n mod 3 = {0, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (361299+5950*sqrt(2))/601^2 for n mod 3 = 1.
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FORMULA
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a(n) = 6*a(n-3)-a(n-6) for n > 6; a(1)=425, a(2)=601, a(3)=1261, a(4)=1289, a(5)=3005, a(6)=7141.
G.f.: (1-x)*(425+1026*x+2287*x^2+1026*x^3+425*x^4) / (1-6*x^3+x^6).
a(3*k-1) = 601*A001653(k) for k >= 1.
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EXAMPLE
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(-297, a(1)) = (-297, 425) is a solution: (-297)^2+(-297+601)^2 = 88209+92416 = 180625 = 425^2.
(A111258(1), a(2)) = (0, 601) is a solution: 0^2+(0+601)^2 = 361201 = 601^2.
(A111258(3), a(4)) = (560, 1289) is a solution: 560^2+(560+601)^2 = 313600+1347921 = 1661521 = 1289^2.
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PROGRAM
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(PARI) {forstep(n=-300, 10000000, [3, 1], if(issquare(2*n^2+1202*n+361201, &k), print1(k, ", ")))}
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CROSSREFS
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Cf. A111258, A001653, A156035 (decimal expansion of 3+2*sqrt(2)), A160099 (decimal expansion of (843+418*sqrt(2))/601), A160100 (decimal expansion of (361299+5950*sqrt(2))/601^2).
Sequence in context: A091293 A134218 A091292 this_sequence A048922 A045094 A054984
Adjacent sequences: A160095 A160096 A160097 this_sequence A160099 A160100 A160101
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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), May 18 2009
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