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A127031
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Let f(n) = exp(Pi*sqrt(n)); sequence gives numbers n such that f(n) - floor(f(n)) < 1/10^6.
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11
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652, 2608, 880111, 2720885, 4089051, 4619054, 5046630, 5409046, 5433402, 5603556, 5645558, 7278138, 7466589, 10037029, 10730786, 10823358, 11540978, 11860073, 12898258, 14554227, 15107659, 15602035, 15896143, 17070573, 18204473, 19252185, 19425342, 19556500
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OFFSET
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1,1
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COMMENTS
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a(212)=195246501 is the smallest integer such that the fractional part of e^(Pi*sqrt(n)) begins with exactly 8 zeros. - Anthony Canu, Oct 11 2017
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LINKS
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EXAMPLE
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5 is not in the sequence since exp(Pi*sqrt(5)) = 1124.186... has fractional part 0.186... which is greater than 1/10^6. But exp(Pi*sqrt(652)) has fractional part 0.0000000001637... which is less than 1/10^6, so 652 is in the sequence. - Michael B. Porter, Aug 24 2016
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MATHEMATICA
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$MaxExtraPrecision = 1000; a = {}; Do[If[((Exp[Pi Sqrt[x]] - Floor[Exp[Pi Sqrt[x]]]) > 0) && ((Exp[Pi Sqrt[x]] - Floor[Exp[Pi Sqrt[x]]]) < 10^(-6)), AppendTo[a, x]], {x, 1, 100000}]; a
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PROG
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(PARI) search(a, b)=my(t, prec=default(realprecision), nprec=round(Pi*sqrt(b)/log(10)+20)); default(realprecision, nprec); for(n=floor(a), b, t=exp(Pi*sqrt(n)); if(t-floor(t)<.000001, print(n))); default(realprecision, prec) \\ Charles R Greathouse IV, Jul 28 2009
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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