cp's OEIS Frontend

A127020 Let f(n) = exp(Pi*sqrt(n)); sequence gives numbers n such that ceiling(f(n))-f(n) < 1/10.

%I A127020 #9 Sep 08 2022 08:45:29
%S A127020 6,7,13,17,18,22,25,27,28,31,37,43,58,59,67,74,84,88,94,125,127,129,
%T A127020 136,149,162,163,174,177,183,213,217,232,240,247,267,273,279,282,295,
%U A127020 301,304,307,321,322,326,333,337,352,355,357,365,385,386,388,389,396,439
%N A127020 Let f(n) = exp(Pi*sqrt(n)); sequence gives numbers n such that ceiling(f(n))-f(n) < 1/10.
%H A127020 G. C. Greubel, <a href="/A127020/b127020.txt">Table of n, a(n) for n = 1..10000</a>
%t A127020 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^(-1)), AppendTo[a, x]], {x, 1, 1000}]; a
%t A127020 epQ[n_]:=Module[{c=Exp[Pi Sqrt[n]]},Ceiling[c]-c<1/10]; Select[ Range[ 500], epQ] (* _Harvey P. Dale_, May 10 2015 *)
%o A127020 (PARI) default(realprecision, 500); c(n) = exp(Pi*sqrt(n));
%o A127020 for(n=1, 500, if( ceil(c(n)) - c(n) <1/10, print1(n", "))) \\ _G. C. Greubel_, May 31 2019
%o A127020 (Magma) SetDefaultRealField(RealField(500)); R:= RealField(); [n: n in [1..500] | Ceiling(Exp(Pi(R)*Sqrt(n))) - Exp(Pi(R)*Sqrt(n)) lt 1/10]; // _G. C. Greubel_, May 31 2019
%Y A127020 Cf. A035484, A127022, A127023, A127024, A127025.
%K A127020 nonn
%O A127020 1,1
%A A127020 _Artur Jasinski_, Jan 03 2007