A330188 - OEIS

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

(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

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: A297834 A376356 A036789 * A214047 A241566 A002960

Adjacent sequences: A330185 A330186 A330187 * A330189 A330190 A330191

KEYWORD

nonn

AUTHOR

Sebastian F. Orellana, Dec 04 2019

STATUS

approved