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 A126689 #45 Jun 23 2021 09:05:27
%S A126689 6,5,6,9,9,9,0,1,3,7,1,6,9,2,7,8,6,8,2,7,9,1,2,0,0,5,6,8,8,9,5,7,5,7,
%T A126689 8,0,7,5,5,4,7,4,1,9,1,5,4,0,8,9,8,3,1,6,5,7,1,5,7,7,8,1,6,3,5,2,6,0,
%U A126689 2,7,8,8,8,1,1,3,8,2,8,4,4,0,2,4,0,5,7,6,0,3,8,2,6,3,9,8,3,6,5,3,8,7,1,5,2
%N A126689 Decimal expansion of negative of Granville-Soundararajan constant.
%C A126689 For any completely multiplicative function f(n) with -1 <= f(n) <= 1, the sum f(1) + f(2) + ... + f(x) is at most (c + o(1))x, where c is this constant. Further, this bound is sharp in that for any c0 > c there are infinitely many f and arbitrarily large x giving a sum less than c0*x. - _Charles R Greathouse IV_, May 26 2015
%C A126689 Named after the British mathematician Andrew James Granville (b. 1962) and the Indian-American mathematician Kannan Soundararajan (b. 1973). - _Amiram Eldar_, Jun 23 2021
%D A126689 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, section 2.33, p. 206.
%H A126689 Vincenzo Librandi, <a href="/A126689/b126689.txt">Table of n, a(n) for n = 0..2000</a>
%H A126689 Antal Balog, Andrew Granville and Kannan Soundararajan, <a href="https://doi.org/10.1007/s40316-013-0001-z">Multiplicative functions in arithmetic progressions</a>, Annales mathématiques du Québec, Vol. 37, No. 1 (2013), pp. 3-30, see p. 10; <a href="https://arxiv.org/abs/math/0702389">arXiv preprint</a>, arXiv:math/0702389 [math.NT], 2007, see p. 7.
%H A126689 Andrew Granville and Kannan Soundararajan, <a href="https://www.jstor.org/stable/2661346">The spectrum of multiplicative functions</a>, Annals of Mathematics, Vol. 153, No. 2 (2001), pp. 407-470, <a href="http://www.dms.umontreal.ca/~andrew/PDF/Spectrum.pdf">alternative link</a>.
%F A126689 Equals 1-2*log[1+sqrt e]+4*Integral_{t=1..sqrt e}([log t]/(1+t)) dt = 1-log 4+4*Sum_{s>=1} K(s)/(s*2^s) where K(s)=Sum_{k=0..s} binomial(s,k)*(-1)^k*[exp(k/2)-1]/k. - _R. J. Mathar_, Feb 16 2007
%F A126689 Equals 1 - 2 * A143301. - _Amiram Eldar_, Aug 25 2020
%e A126689 -0.65699901371692786827912005688957578075547419154089...
%p A126689 Digits := 40 ; K := proc(s) 0.5+add( binomial(s,k)*(-1)^k/k*(exp(0.5*k)-1),k=1..s) ; end: A126689 := proc(smax) 1.0-log(4.0)+add(K(s)*2^(2-s)/s,s=1..smax) ; end: for smax from 0 to 2*Digits do print(A126689(smax)) ; od ; # _R. J. Mathar_, Feb 16 2007
%p A126689 read("transforms3") ; Digits := 120 : x := 1+Pi^2/3+4*dilog(exp(1/2)+1) ; x := evalf(x) ; CONSTTOLIST(x) ; # _R. J. Mathar_, Sep 20 2009
%t A126689 RealDigits[ N[ 4*PolyLog[2, -Sqrt[E]] + Pi^2/3 + 1, 105]][[1]] (* _Jean-François Alcover_, Nov 08 2012, after _R. J. Mathar_ *)
%o A126689 (PARI) 1-2*log(1+exp(1/2))+4*intnum(t=1,exp(1/2),log(t)/(t+1)) \\ _Charles R Greathouse IV_, Apr 29 2013
%o A126689 (Python)
%o A126689 from mpmath import mp, polylog, sqrt, e, pi
%o A126689 mp.dps=106
%o A126689 print([int(k) for k in list(str(4*polylog(2, -sqrt(e)) + pi**2/3 + 1)[3:-1])]) # _Indranil Ghosh_, Jul 03 2017
%Y A126689 Cf. A143301.
%K A126689 cons,nonn
%O A126689 0,1
%A A126689 _Jonathan Vos Post_, Feb 14 2007
%E A126689 More terms from _R. J. Mathar_, Feb 16 2007, Sep 20 2009