

A019297


Integers k such that abs(e^(Pi*sqrt(n))  k) < 0.01 for some n.


6



1, 1, 2198, 422151, 614552, 2508952, 6635624, 199148648, 884736744, 24591257752, 30197683487, 147197952744, 545518122090, 70292286279654, 39660184000219160, 45116546012289600, 262537412640768744
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


COMMENTS

Old name of sequence was "Integers that are very close to values of exp(Pi*sqrt(n))", which left "very close" undefined. Robert G. Wilson v resolved this problem on Feb 28 2006 with the comment that "'Very close' means to within 0.01."  Jon E. Schoenfield, Mar 21 2015


REFERENCES

H. M. Stark, An Introduction to Number Theory. Markham, Chicago, 1970, p. 179.


LINKS

Table of n, a(n) for n=0..16.


EXAMPLE

e^(Pi*sqrt(163)) = 262537412640768743.99999999999925007259719818568887935385...


MATHEMATICA

f[n_] := Block[{e = Exp[Pi*Sqrt[n]]}, Abs[e  Round[e]]]; Round @ Exp[Pi*Sqrt @ Select[Range[ 1, 200], f @ # < 10^(2) &]] (* Robert G. Wilson v, Feb 28 2006 *)


CROSSREFS

Cf. A019296, A058292, A060295.
Sequence in context: A013799 A013868 A044884 * A044989 A202894 A075455
Adjacent sequences: A019294 A019295 A019296 * A019298 A019299 A019300


KEYWORD

sign


AUTHOR

Roy Williams Clickery (roy(AT)ccsf.caltech.edu)


EXTENSIONS

New name, based on Feb 28 2006 comment from Robert G. Wilson v, from Jon E. Schoenfield, Mar 21 2015
Typos in Mma program corrected by Giovanni Resta, Jun 12 2016


STATUS

approved



