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Search: id:A067873
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| A067873 |
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Numbers x satisfying x^2 - D*y^2 = 1 for more than one value of D distinct from x^2 - 1. |
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1
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| 7, 17, 26, 31, 49, 71, 97, 99, 123, 161, 199, 241, 244, 287, 337, 362, 391, 449, 485, 511, 577
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The sequence contains A056220(n) for n>1. For a given x, solutions (x,y) to x^2 - D*y^2 = 1 do not all stand for the least nontrivial positive solution pair. For instance, x=244 solves the latter equation for D=15 and D=135 with corresponding y=63 and y=21. While (244,21) is indeed the fundamental solution to x^2 - 135*y^2 = 1, (244,63) comes only as the third one after the solution pairs (4,1) and (31,8) to x^2 - 15*y^2 = 1.
Sequence includes mostly odd entries in consecutive pairs. It seems reasonable to conjecture that an even entry e satisfies big omega(E) - omega(E) > 2, where E = e^2 - 1. (See A001222 and A001221)
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CROSSREFS
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Cf. A056220.
Sequence in context: A057183 A076293 A072199 this_sequence A011537 A043517 A017353
Adjacent sequences: A067870 A067871 A067872 this_sequence A067874 A067875 A067876
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KEYWORD
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hard,more,nonn
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AUTHOR
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Lekraj Beedassy (blekraj(AT)yahoo.com), Feb 25 2002
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