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 A164833 #32 Oct 07 2024 06:32:19
%S A164833 0,4,6,1,2,5,4,9,1,4,1,8,7,5,1,5,0,0,0,9,9,2,1,4,3,6,2,1,8,0,8,4,9,5,
%T A164833 7,6,4,8,6,8,9,6,1,0,7,7,4,1,7,6,0,6,0,0,5,6,1,5,2,8,0,6,9,2,9,1,7,8,
%U A164833 0,2,3,9,8,0,0,9,2,8,7,6,7,0,2,5,5,7,2,6,8,9,6,6,9,5,5,5,2,8,9,7,2,6,7,6,7,7,7,0,3,0,3,8,7,4,9,4,5,4,6
%N A164833 Decimal expansion of Pi/8 - log(2)/2.
%C A164833 Digits and formula given at Waldschmidt, p. 4.
%D A164833 Mohammad K. Azarian, Problem 1218, Pi Mu Epsilon Journal, Vol. 13, No. 2, Spring 2010, p. 116. Solution published in Vol. 13, No. 3, Fall 2010, pp. 183-185.
%D A164833 L. B. W. Jolley, Summation of series, Dover Publications Inc. (New York), 1961, p. 46 (series n. 251).
%D A164833 A. J. Van Der Poorten, Effectively computable bounds for the solutions of certain Diophantine equations, Acta Arith., 33 (1977), pp. 195-207.
%H A164833 G. C. Greubel, <a href="/A164833/b164833.txt">Table of n, a(n) for n = 0..10000</a>
%H A164833 Michel Waldschmidt, <a href="http://arxiv.org/abs/0908.4031">Perfect Powers: Pillai's works and their developments</a>, Aug 27, 2009.
%F A164833 Equals Sum_{n>=0} Sum_{m>=0} 1/((4*n+3)^(2*m+1)).
%F A164833 Equals Sum_{k>=1} 1/( (4*k-2)*(4*k-1)*(4*k) ). - _Bruno Berselli_, Mar 17 2014
%e A164833 0.0461254914187515000992143621808495764868961077417606...
%e A164833 1/(2*3*4) + 1/(6*7*8) + 1/(10*11*12) + 1/(14*15*16) + ... [_Bruno Berselli_, Mar 17 2014]
%p A164833 evalf[130]((Pi - 4*log(2))/8 ); # _G. C. Greubel_, Aug 11 2019
%t A164833 Join[{0},RealDigits[Pi/8-Log[2]/2,10,120][[1]]] (* _Harvey P. Dale_, Nov 13 2012 *)
%o A164833 (PARI) default(realprecision, 130); (Pi - 4*log(2))/8 \\ _G. C. Greubel_, Aug 11 2019
%o A164833 (Magma) SetDefaultRealField(RealField(130)); R:= RealField(); (Pi(R)-4*Log(2))/8; // _G. C. Greubel_, Aug 11 2019
%o A164833 (Sage) numerical_approx((pi-4*log(2))/8, digits=130) # _G. C. Greubel_, Aug 11 2019
%Y A164833 Cf. A001597, A019675, A016655.
%Y A164833 Cf. A195909, A195913, A195697. - _Mohammad K. Azarian_, Oct 11 2011
%Y A164833 Cf. A239362: Sum_{k>=1} 1/((3k-2)*(3k-1)*(3k)).
%K A164833 nonn,cons,easy
%O A164833 0,2
%A A164833 _Jonathan Vos Post_, Aug 27 2009
%E A164833 Normalized offset and leading zeros - _R. J. Mathar_, Sep 27 2009