|
| |
|
|
A127025
|
|
Let f(n) = exp(Pi*sqrt(n)); sequence gives numbers n such that ceiling(f(n)) - f(n) < 1/10^6.
|
|
12
|
|
|
|
58, 163, 1467, 478233, 881967, 1053883, 1341615, 1844122, 3498092, 6069493, 6396611, 8707530, 10414308, 13340780, 16039620, 17013933, 17226343, 18577932, 19390220, 21991290, 24529596, 26202225, 26634713, 26651262, 26848308, 27497372, 32149837, 35437319, 35892748
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
The probability of finding two real numbers of the form e ^ (Pi * sqrt (n)) such that their fractional parts begin with exactly 8 nines for n in the interval [220000000, 230000000] is less than 5/1000, yet frac(e^(Pi*sqrt(223341175))) and frac(e^(Pi*sqrt(228220223))) both begin with exactly 8 nines. - Anthony Canu, Dec 22 2017
|
|
|
LINKS
|
Anthony Canu, Table of n, a(n) for n = 1..182
|
|
|
MATHEMATICA
|
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^(-6)), AppendTo[a, x]], {x, 1, 1000}]; a
|
|
|
PROG
|
(PARI) is(n)=my(t); default(realprecision, 40); default(realprecision, Pi*sqrt(n)\log(10)+40); t=exp(Pi*sqrt(n)); ceil(t)-t<1e-6 \\ Charles R Greathouse IV, Feb 20 2012
|
|
|
CROSSREFS
|
Cf. A035484, A127022, A127023, A127024.
Sequence in context: A108750 A044390 A044771 * A235376 A067914 A250800
Adjacent sequences: A127022 A127023 A127024 * A127026 A127027 A127028
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Artur Jasinski, Jan 03 2007
|
|
|
EXTENSIONS
|
a(4)-a(20) from Charles R Greathouse IV, Feb 20 2012
a(21)-a(36) from Charles R Greathouse IV, Feb 23 2012
|
|
|
STATUS
|
approved
|
| |
|
|
