login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A330188 a(n) = round(n^arctan(n!)). 0
1, 2, 5, 8, 12, 17, 21, 26, 32, 37, 43, 50, 56, 63, 70, 78, 86, 94, 102, 111, 119, 128, 138, 147, 157, 167, 177, 188, 198, 209, 220, 231, 243, 254, 266, 278, 291, 303, 316, 328, 341, 355, 368, 382, 395, 409, 423, 437, 452, 466, 481, 496, 511, 526, 542, 557, 573 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Due to the limited range of the inverse tangent function, n^arctan(n!) approaches n^(Pi/2), but never reaches it.
It appears that a(n) = round(n^(Pi/2)) for all n > 5. - Jon E. Schoenfield, Dec 07 2019
LINKS
FORMULA
a(n) = round(n^arctan(n!)).
EXAMPLE
a(1) = 1 because 1^arctan(1!) = 1^arctan(1) = 1^0.785398163... --> 1;
a(2) = 2 because 2^arctan(2!) = 2^arctan(2) = 2^1.1071487... = 2.1541948... --> 2;
a(3) = 5 because 3^arctan(3!) = 3^arctan(6) = 3^1.4056476... = 4.6845121... --> 5.
MATHEMATICA
a[n_] := Round[n^ArcTan[n!]]; Array[a, 57] (* Amiram Eldar, Dec 06 2019 *)
PROG
(JavaScript)
var list = [];
function factorial(b) {
var h = 1;
for (var i = 1; i <= b; i++) {
h=h*i;
}
return(h);
}
for (var i = 1; i < 50; i++) {
var g = Math.pow(i, Math.atan(factorial(i)));
appendItem(list, Math.round(g));
}
console.log(list);
(PARI) a(n) = round(n^atan(n!)); \\ Michel Marcus, Jan 17 2024
CROSSREFS
Sequence in context: A272719 A297834 A036789 * A214047 A241566 A002960
KEYWORD
nonn
AUTHOR
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 19 18:58 EDT 2024. Contains 373507 sequences. (Running on oeis4.)