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.

A143149 Decimal expansion of 5*sqrt(2*Pi)/4.

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%I A143149 #24 Jun 13 2023 04:31:49
%S A143149 3,1,3,3,2,8,5,3,4,3,2,8,8,7,5,0,6,2,8,0,1,9,7,0,6,6,0,6,0,1,3,8,0,6,
%T A143149 5,6,6,2,5,8,7,3,3,4,2,5,7,6,2,4,2,2,8,9,5,7,8,7,4,0,4,4,7,0,4,2,7,8,
%U A143149 6,7,0,6,8,2,5,9,8,0,2,4,6,8,6,8,3,2,4,4,7,9,7,9,7,2,5,7,1,5,8,2,6,4,5
%N A143149 Decimal expansion of 5*sqrt(2*Pi)/4.
%C A143149 Upper bound using Shannon entropy arising in randomly-projected hypercubes.
%H A143149 David L. Donoho and Jared Tanner, <a href="https://doi.org/10.1007/s00454-009-9221-z">Counting the faces of randomly-projected hypercubes and orthants, with applications</a>, Discrete & computational geometry, Vol. 43 (2010), pp. 522-541, see p. 533; <a href="http://arxiv.org/abs/0807.3590">arXiv preprint</a>, arXiv:0807.3590 [math.MG], 2008, see p. 10.
%H A143149 Wikipedia, <a href="http://en.wikipedia.org/wiki/Fresnel_integral">Fresnel Integral</a>.
%H A143149 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A143149 Equals 10*Integral_{x>=0} x*sin(x^4) dx or 10*Integral_{x>=0} x*cos(x^4) dx (Fresnel integrals).
%e A143149 3.13328534328875...
%t A143149 RealDigits[5*Sqrt[2*Pi]/4, 10, 120][[1]] (* _Amiram Eldar_, Jun 13 2023 *)
%o A143149 (PARI) 5*sqrt(2*Pi)/4 \\ _Michel Marcus_, Mar 06 2020
%Y A143149 Apart from possible scaling sqrt(A019692/2^n) for n=0..7 are A019727, A002161, A069998, A019704, A217481, A019706, this sequence, A019710.
%Y A143149 Cf. A143148 (lower bound).
%K A143149 cons,easy,nonn
%O A143149 1,1
%A A143149 _Jonathan Vos Post_, Jul 27 2008
%E A143149 Edited and a(100) corrected by _Georg Fischer_, Jul 16 2021