%I #28 Jun 29 2023 09:02:23
%S 9,8,0,7,8,5,2,8,0,4,0,3,2,3,0,4,4,9,1,2,6,1,8,2,2,3,6,1,3,4,2,3,9,0,
%T 3,6,9,7,3,9,3,3,7,3,0,8,9,3,3,3,6,0,9,5,0,0,2,9,1,6,0,8,8,5,4,5,3,0,
%U 6,5,1,3,5,4,9,6,0,5,0,6,3,9,1,5,0,6,4,9,8,5,8,5,3,3,0,0,7,6,3,2,5,9,8,9,4
%N Decimal expansion of the real part of I^(1/8), or cos(Pi/16).
%C The corresponding imaginary part is in A232738.
%H Stanislav Sykora, <a href="/A232737/b232737.txt">Table of n, a(n) for n = 0..1000</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Trigonometric_constants_expressed_in_real_radicals">Trigonometric constants expressed in real radicals</a>.
%F Equals (1/2) * sqrt(2+sqrt(2+sqrt(2))). - _Seiichi Manyama_, Apr 04 2021
%e 0.9807852804032304491261822361342390369739337308933360950029160885453...
%t RealDigits[Cos[Pi/16], 10, 120][[1]] (* _Amiram Eldar_, Jun 29 2023 *)
%o (PARI) real(I^(1/8)) \\ _Seiichi Manyama_, Apr 04 2021
%o (PARI) cos(Pi/16) \\ _Seiichi Manyama_, Apr 04 2021
%o (PARI) sqrt(2+sqrt(2+sqrt(2)))/2 \\ _Seiichi Manyama_, Apr 04 2021
%Y Cf. A232738 (imaginary part), A010503 (real(I^(1/2))), A010527 (real(I^(1/3))), A144981 (real(I^(1/4))), A019881 (real(I^(1/5))), A019884 (real(I^(1/6))), A232735 (real(I^(1/7))), A019889 (real(I^(1/9))), A019890 (real(I^(1/10))).
%K nonn,cons,easy
%O 0,1
%A _Stanislav Sykora_, Nov 29 2013
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