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Search: id:A060569
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| A060569 |
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Consider Pythagorean triples which satisfy X^2+(X+7)^2=Z^2; sequence gives increasing values of Z. |
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2
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| 13, 17, 73, 97, 425, 565, 2477, 3293, 14437, 19193, 84145, 111865, 490433, 651997, 2858453, 3800117, 16660285, 22148705, 97103257, 129092113, 565959257, 752403973, 3298652285, 4385331725, 19225954453, 25559586377, 112057074433, 148972186537, 653116492145
(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 gives the values of Z in X^2 + Y^2 = Z^2 where Y = X + 7 and gcd(X,Y,Z)=1. The values of X are given by the formula: X(1)=5, X(2)=8, X(3)=48, X(4)=65, X(n) = 6*X(n-2) - X(n-4) + 14 for n >= 5 - see A117474. Also, Y - X = 7, which is the second term in A058529. We have Z(1)=13, Z(2)=17, Z(3)=73, Z(4)=97, Z(n)=6*Z(n-2) - Z(n-4) for n >= 5. - Andras Erszegi (erszegi.andras(AT)chello.hu), Mar 19 2006
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MAPLE
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f:=proc(n) option remember; if n=1 then RETURN(13) fi; if n=2 then RETURN(17) fi; if n=3 then RETURN(73) fi; if n=4 then RETURN(97) fi; 6*f(n-2)-f(n-4); end;
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CROSSREFS
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Sequence in context: A140533 A076789 A089577 this_sequence A108265 A069853 A123909
Adjacent sequences: A060566 A060567 A060568 this_sequence A060570 A060571 A060572
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KEYWORD
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nonn
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AUTHOR
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Sebastiao Antonio da Silva (silseb(AT)ig.com.br), Apr 12 2001
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Oct 06 2007
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