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Search: id:A074294
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| A074294 |
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Integers 1 to 2k followed by integers 1 to 2(k+1) and so on. |
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+0
1
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| 1, 2, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 2
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Comment from Cino Hilliard (hillcino368(AT)gmail.com), Sep 13 2004: "Also the numerator of the fraction in the continued fraction expansion of sqrt(n) for non-square n = 2,3,5,6,7... . E.g. for n = 7,
"sqrt(7).=.2.+._3_................
"...............4..+._3_..........
".....................4..+._3_....
"...........................4.....
"3 is the 5th entry in the table. sqrt(1) and sqrt(4) are not included because 1 and 4 are squares."
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FORMULA
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a(n^2+n)=2n.
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PROGRAM
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(PARI) a(n)=n-2*binomial(floor(1/2+sqrt(n)), 2)
(PARI) gp > c(n) = for(x=2, n, if(issquare(x)==0, a=floor(sqrt(x)); print1(x-a^2", "))) (Cino Hilliard)
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CROSSREFS
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Sequence in context: A066016 A098068 A075425 this_sequence A062050 A046653 A162190
Adjacent sequences: A074291 A074292 A074293 this_sequence A074295 A074296 A074297
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KEYWORD
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nonn,easy
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AUTHOR
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Michael Somos
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