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

Author

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

Keywords

• sign

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

Examples

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

References

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

Crossrefs

Cf. A019296, A058292, A060295.

Programs

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 *)

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