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%I #24 Sep 08 2022 08:45:29
%S 25,37,43,58,67,74,163,232,522,719,1169,1245,1467,1850,1872,2086,3368,
%T 4075,5773,7685,7802,7942,8325,9728,10032,11682,12158,13574,17908,
%U 18505,19183,19396,20039,20244,20584,22241,23773,23778,23834,25004,27573,28071,32497
%N Let f(k) = exp(Pi*sqrt(k)); sequence gives numbers k such that ceiling(f(k)) - f(k) < 1/10^3.
%H JungHwan Min, <a href="/A127022/b127022.txt">Table of n, a(n) for n = 1..5000</a>
%t 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^(-3)), AppendTo[a, x]], {x, 1, 1000}]; a
%t Reap[Block[{$MaxExtraPrecision = Infinity}, Do[If[N[FractionalPart[Exp[Pi Sqrt[n]]], 8] > .999, Sow[n]], {n, 2000}]]][[-1, 1]] (* _JungHwan Min_, Mar 20 2016 *)
%o (PARI) default(realprecision, 500); c(n) = exp(Pi*sqrt(n));
%o for(n=1, 50000, if( ceil(c(n)) - c(n) <1/1000, print1(n", "))) \\ _G. C. Greubel_, Jun 02 2019
%o (Magma) SetDefaultRealField(RealField(500)); R:= RealField(); [n: n in [1..50000] | Ceiling(Exp(Pi(R)*Sqrt(n))) - Exp(Pi(R)*Sqrt(n)) lt 1/1000]; // _G. C. Greubel_, Jun 02 2019
%Y Cf. A035484, A127023, A127024, A127025.
%K nonn
%O 1,1
%A _Artur Jasinski_, Jan 03 2007
%E a(16)-a(43) added (from _JungHwan Min_'s b-file) by _Jon E. Schoenfield_, Sep 04 2017
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