A019296 Values of n for which exp(Pi*sqrt(n)) is very close to an integer.

-1, 0, 6, 17, 18, 22, 25, 37, 43, 58, 59, 67, 74, 103, 148, 149, 163, 164, 177, 205, 223, 226, 232, 267, 268, 326, 359, 386, 522, 566, 630, 638, 652, 719, 790, 792, 928, 940, 986, 1005, 1014, 1169, 1194, 1213, 1245, 1257, 1293, 1326, 1332, 1353, 1441, 1467

Offset

-1,3

Comments

Very close is defined here as being less than 1/100.

e^(Pi*sqrt(163)) is 262537412640768743.9999999999992500725971981856888... and no closer exponent of this character has been discovered. See A069014.

Links

Table of n, a(n) for n=-1..50.

Mathematica

Select[ Range[ -1, 1480], Abs[ Round[E^(Pi*Sqrt[ # ])] - E^(Pi*Sqrt[ # ])] < 0.01 &]

Prog

(Contribution from M. F. Hasler, Jan 26 2014) (Start)
/* Adjusting the p-value allows one to select more interesting subsequences. */
(PARI) is_A019296(n, p=2)=abs(frac(exp(sqrt(n)*Pi))-.5)>.5-.1^p
(PARI) {p=.5-.1^2; for(n=1, 9e9, abs(frac(exp(sqrt(n)*Pi))-.5)>p&&print1(round(exp(sqrt(n)*Pi))", ")) \\ (End)

Crossrefs

Cf. A003173, A019297, A035484, A069014.

Sequence in context: A112366 A095421 A063584 * A035484 A277684 A009171

Adjacent sequences: A019293 A019294 A019295 * A019297 A019298 A019299

Keyword

sign

Author

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

Extensions

Edited and extended by Robert G. Wilson v, Sep 07 2003

Status

approved