cp's OEIS Frontend

A343057 Decimal expansion of tan(Pi/32).

%I A343057 #35 Feb 20 2025 10:23:13
%S A343057 0,9,8,4,9,1,4,0,3,3,5,7,1,6,4,2,5,3,0,7,7,1,9,7,5,2,1,2,9,1,3,2,7,4,
%T A343057 3,2,2,9,3,0,5,2,4,5,0,6,9,9,2,0,2,6,9,5,9,8,0,9,1,6,1,2,1,1,3,4,4,1,
%U A343057 9,4,3,8,7,3,0,8,1,2,9,7,2,2,5,6,4,8,5,2,1,4,1,8,0,3,7,3,6,0,0,1,3,7,0,6,7,1,6,9,7,7,9,1,7,6,5
%N A343057 Decimal expansion of tan(Pi/32).
%H A343057 G. C. Greubel, <a href="/A343057/b343057.txt">Table of n, a(n) for n = 0..10000</a>
%H A343057 Wikipedia, <a href="https://en.wikipedia.org/wiki/Trigonometric_constants_expressed_in_real_radicals">Trigonometric constants expressed in real radicals</a>
%H A343057 <a href="/index/Al#algebraic_08">Index entries for algebraic numbers, degree 8</a>.
%F A343057 Equals sqrt( (2-sqrt(2+sqrt(2+sqrt(2))))/(2+sqrt(2+sqrt(2+sqrt(2)))) ).
%e A343057 0.098491403357164253077197...
%t A343057 RealDigits[Tan[Pi/32], 10, 120, -1][[1]] (* _Amiram Eldar_, Apr 27 2021 *)
%o A343057 (PARI) tan(Pi/32)
%o A343057 (PARI) sqrt((2-sqrt(2+sqrt(2+sqrt(2))))/(2+sqrt(2+sqrt(2+sqrt(2)))))
%o A343057 (Magma) R:= RealField(125); Tan(Pi(R)/32); // _G. C. Greubel_, Sep 30 2022
%o A343057 (SageMath) numerical_approx(tan(pi/32), digits=125) # _G. C. Greubel_, Sep 30 2022
%Y A343057 Cf. A343055 (sin(Pi/32)), A343056 (cos(Pi/32)).
%Y A343057 tan(Pi/m): A002194 (m=3), A019934 (m=5), A020760 (m=6), A343058 (m=7), A188582 (m=8), A019918 (m=9), A019916 (m=10), A019913 (m=12), A343059 (m=14), A019910 (m=15), A343060 (m=16), A343061 (m=17), A019908 (m=18), A019907 (m=20), A343062 (m=24), A019904 (m=30), A343057 (m=32), A019903 (m=36).
%K A343057 nonn,cons,easy
%O A343057 0,2
%A A343057 _Seiichi Manyama_, Apr 04 2021