cp's OEIS Frontend

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.

A158241 Decimal expansion of theta = arctan((sqrt(10-2*sqrt(5))-2)/(sqrt(5)-1)).

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%I A158241 #29 Nov 20 2024 23:48:51
%S A158241 2,7,6,7,8,7,1,7,9,4,4,8,5,2,2,6,2,5,7,5,4,2,6,6,3,6,5,0,4,4,6,3,4,2,
%T A158241 6,0,0,1,7,5,1,1,9,1,1,3,5,0,3,5,8,1,6,1,6,6,9,1,3,4,8,0,1,8,5,8,4,2,
%U A158241 7,5,8,4,7,4,4,3,4,0,6,9,8,5,0,3,3,5,4,2,8,2,1,7,1,5,4,2,6,6,0,3,5,8,6,3
%N A158241 Decimal expansion of theta = arctan((sqrt(10-2*sqrt(5))-2)/(sqrt(5)-1)).
%C A158241 This number arose in the Davenport-Heilbronn zeta-function which satisfies a functional equation (like zeta) but does not satisfy RH. Some nontrivial zeros are off the critical line (see reference).
%D A158241 P. Borwein et al., The Riemann Hypothesis, Springer (2009), 136-137.
%H A158241 E. Bombieri and D. Hejhal, <a href="http://gallica.bnf.fr/ark:/12148/bpt6k5744593d/f13.image">Sur les zéros des fonctions zeta d'Epstein</a>, (mostly in English) Comptes rendus de l'Académie des Sciences, Paris, 304 (1987), 213-217.
%H A158241 H. Davenport and H. Heilbronn, <a href="https://doi.org/10.1112/jlms/s1-11.3.181">On the zeros of certain Dirichlet series I</a>, J. London Math. Soc. 11 (1936), 181-185.
%H A158241 H. Davenport and H. Heilbronn, <a href="https://doi.org/10.1112/jlms/s1-11.4.307">On the zeros of certain Dirichlet series II</a>, J. London Math. Soc. 11 (1936), 307-312.
%H A158241 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e A158241 0.27678717...
%t A158241 RealDigits[ArcTan[(Sqrt[10-2*Sqrt[5]]-2)/(Sqrt[5]-1)],10,120][[1]] (* _Harvey P. Dale_, Mar 03 2018 *)
%o A158241 (PARI) atan((sqrt(10-2*sqrt(5))-2)/(sqrt(5)-1)) \\ _Charles R Greathouse IV_, Mar 10 2016
%K A158241 cons,nonn
%O A158241 0,1
%A A158241 _Benoit Cloitre_, Mar 14 2009
%E A158241 Keyword:cons inserted, leading zero and offset adjusted by _R. J. Mathar_, Jul 15 2010