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 A343056 #42 Aug 31 2025 10:19:18 %S A343056 9,9,5,1,8,4,7,2,6,6,7,2,1,9,6,8,8,6,2,4,4,8,3,6,9,5,3,1,0,9,4,7,9,9, %T A343056 2,1,5,7,5,4,7,4,8,6,8,7,2,9,8,5,7,0,6,1,8,3,3,6,1,2,9,6,5,7,8,4,8,9, %U A343056 0,1,6,6,8,9,4,5,8,6,5,3,7,9,7,2,5,2,9,0,8,4,2,6,9,6,4,8,3,9,0,2,8,7,7,2,4,4,9,3,1,1,8,2,9 %N A343056 Decimal expansion of the real part of i^(1/16), or cos(Pi/32). %H A343056 G. C. Greubel, <a href="/A343056/b343056.txt">Table of n, a(n) for n = 0..10000</a> %H A343056 Leon D. Fairbanks, <a href="https://arxiv.org/abs/2308.04437">Powers of Cosine and Sine</a>, arXiv:2308.04437 [math.GM], 2023. See p. 3. %H A343056 Wikipedia, <a href="https://en.wikipedia.org/wiki/Trigonometric_constants_expressed_in_real_radicals">Trigonometric constants expressed in real radicals</a>. %H A343056 <a href="/index/Al#algebraic_16">Index entries for algebraic numbers, degree 16</a> %F A343056 Equals (1/2) * sqrt(2+sqrt(2+sqrt(2+sqrt(2)))). %F A343056 Satisfies 32768*x^16 -131072*x^14 +212992*x^12 -180224*x^10 +84480*x^8 -21504*x^6 +2688*x^4 -128*x^2 +1 = 0. - _R. J. Mathar_, Aug 29 2025 %F A343056 Equals 2F1(-1/16,1/16;1/2;1/2). - _R. J. Mathar_, Aug 31 2025 %e A343056 0.9951847266721968862448369... %t A343056 RealDigits[Cos[Pi/32], 10, 100][[1]] (* _Amiram Eldar_, Apr 27 2021 *) %o A343056 (PARI) real(I^(1/16)) %o A343056 (PARI) cos(Pi/32) %o A343056 (PARI) sqrt(2+sqrt(2+sqrt(2+sqrt(2))))/2 %o A343056 (Magma) R:= RealField(127); Cos(Pi(R)/32) // _G. C. Greubel_, Sep 30 2022 %o A343056 (SageMath) numerical_approx(cos(pi/32), digits=122) # _G. C. Greubel_, Sep 30 2022 %Y A343056 cos(Pi/m): A010503 (m=4), A019863 (m=5), A010527 (m=6), A073052 (m=7), A144981 (m=8), A019879 (m=9), A019881 (m=10), A019884 (m=12), A232735 (m=14), A019887 (m=15), A232737 (m=16), A210649 (m=17), A019889 (m=18), A019890 (m=20), A144982 (m=24), A019893 (m=30). this sequence (m=32), A019894 (m=36). %K A343056 nonn,cons,easy,changed %O A343056 0,1 %A A343056 _Seiichi Manyama_, Apr 04 2021