This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A232737 #36 Aug 31 2025 10:17:13 %S A232737 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 A232737 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 A232737 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 A232737 Decimal expansion of the real part of I^(1/8), or cos(Pi/16). %C A232737 The corresponding imaginary part is in A232738. %H A232737 Stanislav Sykora, <a href="/A232737/b232737.txt">Table of n, a(n) for n = 0..1000</a> %H A232737 Wikipedia, <a href="https://en.wikipedia.org/wiki/Trigonometric_constants_expressed_in_real_radicals">Trigonometric constants expressed in real radicals</a>. %H A232737 <a href="/index/Al#algebraic_08">Index entries for algebraic numbers, degree 8</a> %F A232737 Equals (1/2) * sqrt(2+sqrt(2+sqrt(2))). - _Seiichi Manyama_, Apr 04 2021 %F A232737 Root of 128*x^8 -256*x^6 +160*x^4 -32*x^2 +1 = 0. - _R. J. Mathar_, Aug 29 2025 %F A232737 2*this^2 -1 = A144981. - _R. J. Mathar_, Aug 29 2025 %F A232737 Equals 2F1(-1/8,1/8;1/2;1/2). - _R. J. Mathar_, Aug 31 2025 %e A232737 0.9807852804032304491261822361342390369739337308933360950029160885453... %t A232737 RealDigits[Cos[Pi/16], 10, 120][[1]] (* _Amiram Eldar_, Jun 29 2023 *) %o A232737 (PARI) real(I^(1/8)) \\ _Seiichi Manyama_, Apr 04 2021 %o A232737 (PARI) cos(Pi/16) \\ _Seiichi Manyama_, Apr 04 2021 %o A232737 (PARI) sqrt(2+sqrt(2+sqrt(2)))/2 \\ _Seiichi Manyama_, Apr 04 2021 %Y A232737 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 A232737 nonn,cons,easy,changed %O A232737 0,1 %A A232737 _Stanislav Sykora_, Nov 29 2013