A019297 Integers k such that abs(e^(Pi*sqrt(n)) - k) < 0.01 for some n.

-1, 1, 2198, 422151, 614552, 2508952, 6635624, 199148648, 884736744, 24591257752, 30197683487, 147197952744, 545518122090, 70292286279654, 39660184000219160, 45116546012289600, 262537412640768744

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