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Search: id:A134420
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| A134420 |
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Composite square-free numbers of the form n^2 + 1. |
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+0
1
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| 10, 26, 65, 82, 122, 145, 170, 226, 290, 362, 442, 485, 530, 626, 730, 785, 842, 901, 962, 1090, 1157, 1226, 1370, 1522, 1765, 1937, 2026, 2117, 2210, 2305, 2402, 2501, 2602, 2705, 2810, 3026, 3365, 3482, 3601, 3722, 3845, 3970, 4097, 4226, 4490, 4762
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Square roots of these numbers are quadratic irrationals and corresponding chain fraction reresentations are periodic: sqrt(10) = [3;{2,3}], sqrt(26) = [5;{2,5}], sqrt(65) = [8;{2,8}], ..., where {} is denoted a period (we write {6} == {2,3}).
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EXAMPLE
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a(1)=10 because 10 = 3^2 + 1 is a square-free number,
a(2)=26 because 26 = 5^2 + 1 is a square-free number,
a(3)=65 becasue 65 = 8^2 + 1 is square-free.
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MAPLE
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ts_fn3:=proc(n) local i, tren, ans; ans:=[ ]: for i from 1 to n do tren := i^(2)+1: if (isprime(tren) = false and numtheory[mobius] (tren) <> 0 ) then ans:=[ op(ans), tren ]: fi od: RETURN(ans) end: ts_fn3(200);
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CROSSREFS
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Cf. A002496, A124809.
Sequence in context: A074789 A125075 A055710 this_sequence A144255 A072379 A005970
Adjacent sequences: A134417 A134418 A134419 this_sequence A134421 A134422 A134423
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KEYWORD
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nonn
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AUTHOR
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Jani Melik (jani_melik(AT)hotmail.com), Jan 18 2008
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EXTENSIONS
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Definition corrected by T. D. Noe, Sep 16 2008
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