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A087057
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Smallest number whose square is larger than 2*n^2.
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7
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2, 3, 5, 6, 8, 9, 10, 12, 13, 15, 16, 17, 19, 20, 22, 23, 25, 26, 27, 29, 30, 32, 33, 34, 36, 37, 39, 40, 42, 43, 44, 46, 47, 49, 50, 51, 53, 54, 56, 57, 58, 60, 61, 63, 64, 66, 67, 68, 70, 71, 73, 74, 75, 77, 78, 80, 81, 83, 84, 85, 87, 88, 90, 91, 92, 94, 95, 97, 98, 99, 101
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Integer solutions to the equation x=ceiling(r*floor(x/r)) where r=sqrt(2) - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 14 2004
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FORMULA
| a(n) = 1 + A001951(n) = 1 + floor[n*sqrt(2)] = sqrt(A087058(n)).
a(n) = ceiling(n*sqrt(2)). - Vincenzo Librandi, Oct 22 2011
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EXAMPLE
| a(10) = 15 because the 15^2 = 225 is the smallest square number greater than 2*10^2 = 200.
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PROG
| (PARI) a(n)=ceil(n*sqrt(2)) \\ Charles R Greathouse IV, Oct 24 2011
(PARI) a(n)=sqrtint(2*n^2+sqrtint(8*n^2)+1) \\ Charles R Greathouse IV, Oct 24 2011
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CROSSREFS
| Cf. A001951, A087055, A087056, A087058, A087059, A087060.
Sequence in context: A039033 A047333 A032796 * A184580 A184622 A195129
Adjacent sequences: A087054 A087055 A087056 * A087058 A087059 A087060
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KEYWORD
| easy,nonn
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AUTHOR
| Jens Voss (jens(AT)voss-ahrensburg.de), Aug 07 2003
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