Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #32 Mar 03 2020 09:50:03
%S 3,1,4,1,5,9,0,6,5,3,5,8,9,7,9,3,2,4,0,4,6,2,6,4,3,3,8,3,2,6,9,5,0,2,
%T 8,8,4,1,9,7,2,9,1,3,9,9,3,7,5,1,0,3,0,5,0,9,7,4,9,4,4,6,9,3,3,4,9,8,
%U 1,6,4,0,0,8,8,0,6,7,8,9,9,9,0,2,6,7,5,6,7,8,7,3,0,3,3,3,4,0,4,3,6,9,6,9,5
%N Decimal expansion of 4*Sum_{k=1..500000} (-1)^(k-1)/(2k-1).
%C An approximation to Pi.
%C A case of "high precision fraud": curiously, among the first 40 digits, only 4 are wrong (in positions 7, 18, 19 and 30). - _Jean-François Alcover_, Apr 23 2013
%C This result arises because the sum is Pi - 2*10^-6 + 2*10^-18 - 10^-29 + 122*10^-42 - ... - _Jon E. Schoenfield_, Mar 11 2018
%H J. M. Borwein and P. B. Borwein, <a href="http://www.jstor.org/stable/2324993">Strange series and high precision fraud</a>, Amer. Math. Monthly 99, 7 (Aug. 1992), 622-640.
%H J. M. Borwein, P. B. Borwein and K. Dilcher, <a href="http://www.jstor.org/stable/2324715">Pi, Euler numbers and asymptotic expansions</a>, Amer. Math. Monthly, 96 (1989), 681-687.
%H J. M. Borwein and R. M. Corless, <a href="http://www.cecm.sfu.ca/~jborwein/sloane/sloane.html">Review of "An Encyclopedia of Integer Sequences" by N. J. A. Sloane and Simon Plouffe</a>, SIAM Review, 38 (1996), 333-337.
%e 3.1415906535897932404626433832695028841972913993751030509749446933498...
%o (PARI) 4*sum(k=1, 500000, (-1.)^(k-1)/(2*k-1)) \\ _Michel Marcus_, Mar 11 2018
%Y Cf. A000796, A216542, A013706, A216543, A216544, A216545, A013705, A216546, A216547, A216548.
%Y Cf. also A195793.
%K cons,nonn
%O 1,1
%A _N. J. A. Sloane_
%E a(78)-a(80) corrected and more digits from _Jon E. Schoenfield_, Mar 11 2018