A345670 -id:A345670 - cp's OEIS frontend

A346151 a(n) is the smallest integer k > 0 such that 1 - tanh(k) < 10^(-n).

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Treanungkur Mal, Jul 07 2021

nonn

As k increases, 1 - tanh(k) rapidly approaches 2*exp(-2*k), and the smallest integer k such that 2*exp(-2*k) < 10^(-n), i.e., such that k > (n*log(10) + log(2))/2, is simply ceiling((1/2)*(n*log(10) + log(2))). It seems very likely that this expression gives a(n) for all n >= 0. - Jon E. Schoenfield, Jul 08 2021

			For n = 3, a(3) = 4 because 4 is the smallest positive integer k such that 1 - tanh(k) < 10^(-3): 1 - tanh(4) = 0.00067....

Cf. A346033 (sin), A345670 (cos).

a[0] = 1; a[n_] := Ceiling @ ArcTanh[1 - 10^(-n)]; Array[a, 100, 0] (* Amiram Eldar, Jul 12 2021 *)

cp's OEIS Frontend

A346151 a(n) is the smallest integer k > 0 such that 1 - tanh(k) < 10^(-n).

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