A346166 a(n) is the smallest integer k >= 0 such that cosh(k) > 10^(n^2).

1, 3, 10, 22, 38, 59, 84, 114, 149, 188, 231, 280, 333, 390, 452, 519, 591, 667, 747, 832, 922, 1017, 1116, 1219, 1327, 1440, 1558, 1680, 1806, 1938, 2074, 2214, 2359, 2509, 2663, 2822, 2985, 3153, 3326, 3503, 3685, 3872, 4063, 4259, 4459, 4664, 4873, 5088

Offset

0,2

Links

Table of n, a(n) for n=0..47.

Formula

a(n) = 1 + floor(arccosh(10^(n^2))). - Jon E. Schoenfield, Jul 08 2021

Example

For n = 4, a(4) = 38 because 38 is the smallest positive integer k such that cosh(k) > 10^(16): cosh(38) = 1.59...*10^16, which is greater than 10^(4^2), i.e., 10^16.

Mathematica

a[0] = 1; a[n_] := Ceiling @ ArcCosh[10^(n^2)]; Array[a, 50, 0] (* Amiram Eldar, Jul 12 2021 *)

Prog

(PARI) a(n) = 1 + floor(acosh(10^(n^2))); \\ Michel Marcus, Aug 24 2021

Crossrefs

Sequence in context: A190092 A174459 A326124 * A122795 A140066 A006503

Adjacent sequences: A346163 A346164 A346165 * A346167 A346168 A346169

Keyword

nonn,less

Author

Treanungkur Mal, Jul 08 2021

Extensions

More terms from Jinyuan Wang, Jul 08 2021

Status

approved