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

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, 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, 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

Offset

1,1

Comments

Upper bound using Shannon entropy arising in randomly-projected hypercubes.

Links

Table of n, a(n) for n=1..103.

David L. Donoho and Jared Tanner, Counting the faces of randomly-projected hypercubes and orthants, with applications, Discrete & computational geometry, Vol. 43 (2010), pp. 522-541, see p. 533; arXiv preprint, arXiv:0807.3590 [math.MG], 2008, see p. 10.

Wikipedia, Fresnel Integral.

Index entries for transcendental numbers.

Formula

Equals 10*Integral_{x>=0} x*sin(x^4) dx or 10*Integral_{x>=0} x*cos(x^4) dx (Fresnel integrals).

Example

3.13328534328875...

Mathematica

RealDigits[5*Sqrt[2*Pi]/4, 10, 120][[1]] (* Amiram Eldar, Jun 13 2023 *)

Prog

(PARI) 5*sqrt(2*Pi)/4 \\ Michel Marcus, Mar 06 2020

Crossrefs

Apart from possible scaling sqrt(A019692/2^n) for n=0..7 are A019727, A002161, A069998, A019704, A217481, A019706, this sequence, A019710.

Cf. A143148 (lower bound).

Sequence in context: A328776 A110629 A119979 * A268498 A059787 A081325

Adjacent sequences: A143146 A143147 A143148 * A143150 A143151 A143152

Keyword

cons,easy,nonn

Author

Jonathan Vos Post, Jul 27 2008

Extensions

Edited and a(100) corrected by Georg Fischer, Jul 16 2021

Status

approved