A330188 a(n) = round(n^arctan(n!)).

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

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

Table of n, a(n) for n=1..57.

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

Adjacent sequences: A330185 A330186 A330187 * A330189 A330190 A330191

Keyword

nonn

Author

Sebastian F. Orellana, Dec 04 2019

Status

approved