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A127025
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Let f(n) = exp(Pi*sqrt(n)); sequence gives numbers n such that ceiling(f(n)) - f(n) < 1/10^6.
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12
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58, 163, 1467, 478233, 881967, 1053883, 1341615, 1844122, 3498092, 6069493, 6396611, 8707530, 10414308, 13340780, 16039620, 17013933, 17226343, 18577932, 19390220, 21991290, 24529596, 26202225, 26634713, 26651262, 26848308, 27497372, 32149837, 35437319, 35892748
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OFFSET
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1,1
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COMMENTS
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The probability of finding two real numbers of the form e^(Pi*sqrt(n)) whose fractional parts begin with exactly 8 nines for n in the interval [220000000, 230000000] is less than 5/1000, yet frac(e^(Pi*sqrt(223341175))) and frac(e^(Pi*sqrt(228220223))) both begin with exactly 8 nines. - Anthony Canu, Dec 22 2017
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LINKS
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Anthony Canu, Table of n, a(n) for n = 1..182
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MATHEMATICA
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a = {}; Do[If[(1 - (Exp[Pi Sqrt[x]] - Floor[Exp[Pi Sqrt[x]]]) > 0) && (1 - ( Exp[Pi Sqrt[x]] - Floor[Exp[Pi Sqrt[x]]])< 10^(-6)), AppendTo[a, x]], {x, 1, 1000}]; a
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PROG
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(PARI) is(n)=my(t); default(realprecision, 40); default(realprecision, Pi*sqrt(n)\log(10)+40); t=exp(Pi*sqrt(n)); ceil(t)-t<1e-6 \\ Charles R Greathouse IV, Feb 20 2012
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CROSSREFS
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Cf. A035484, A127022, A127023, A127024.
Sequence in context: A108750 A044390 A044771 * A235376 A067914 A250800
Adjacent sequences: A127022 A127023 A127024 * A127026 A127027 A127028
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KEYWORD
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nonn
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AUTHOR
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Artur Jasinski, Jan 03 2007
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EXTENSIONS
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a(4)-a(20) from Charles R Greathouse IV, Feb 20 2012
a(21)-a(36) from Charles R Greathouse IV, Feb 23 2012
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STATUS
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approved
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