%I #24 Apr 05 2020 04:56:17
%S 1,9,23,51,79,253,270,320,366,2460,3844,14207,46819,68493
%N Fractional part of 1/(1-tanh(n)) decreases monotonically to zero.
%t $MaxExtraPrecision = Infinity; t = 1; Do[s = FractionalPart[1/(1 - Tanh[n])]; If[s < t, Print[n]; t = s;], {n, 1, 5000}]; (* _Vaclav Kotesovec_, Apr 05 2020 *)
%o (PARI) lista(nn) = {my(b=8, r=1); print1(1); for(n=1, nn, until(frac(1/(1-tanh(b)))<r, b++; default(realprecision, 2*b)); print1(", ", b); r=frac(1/(1-tanh(b)))); } \\ Modified by _Jinyuan Wang_, Apr 04 2020
%Y Cf. A046947 (for abs(sin(n))).
%K nonn,more
%O 0,2
%A _Benoit Cloitre_, Feb 01 2003
%E a(8)-a(10) from _Jinyuan Wang_, Apr 03 2020
%E a(11)-a(13) from _Vaclav Kotesovec_, Apr 05 2020