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 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 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

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