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%I #102 Oct 29 2023 09:47:43
%S 1,1,0,0,1,0,0,1,0,0,0,0,1,1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,
%T 1,0,0,0,0,1,0,1,1,0,1,0,0,0,1,1,0,0,0,0,1,0,0,0,1,1,0,1,0,0,1,1,0,0,
%U 0,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1
%N Expansion of Pi in base 2 (or, binary expansion of Pi).
%D J. P. Delahaye, Le Fascinant Nombre Pi, "100000 digits of pi in base two", pp. 209-210; Pour la Science, Paris 1997.
%H Vincenzo Librandi, <a href="/A004601/b004601.txt">Table of n, a(n) for n = 2..1000</a>
%H Francisco Javier Aragón Artacho, <a href="http://gigapan.org/gigapans/93389">2 billion step walk on the digits of pi</a>
%H A. Brouty, <a href="http://www.brouty.fr/Maths/pi2.html">Les décimales de pi en base 2 jusqu'à 1 million</a>
%H Elias's Pi Page, <a href="http://www.befria.nu/elias/pi/">Binary representation of pi with 32768 digits</a>
%H J. Leroy, M. Rigo, and M. Stipulanti, <a href="https://doi.org/10.37236/6581">Behavior of Digital Sequences Through Exotic Numeration Systems</a>, Electronic Journal of Combinatorics 24(1) (2017), #P1.44. See w(n) in Example 19.
%H Steve Pagliarulo, <a href="https://web.archive.org/web/20160324234131/http://members.shaw.ca/francislyster/pi/pistats/pibase2.pdf">Stu's pi page: base 2</a> (23 pages) [link was dead, retrieved from the Internet archive]
%e 11.0010010000111111011010101000100010000...
%p convert(evalf(Pi), binary, 120); # _Alois P. Heinz_, Dec 16 2018
%t RealDigits[Pi, 2, 75][[1]]
%t Table[ResourceFunction["NthDigit"][Pi, n, 2], {n, 1, 100}] (* _Joan Ludevid_, Jun 24 2022;easy to compute a(10000000)=0 with this function; requires Mathematica 12.0+ *)
%o (PARI) binary(Pi) \\ _Altug Alkan_, Apr 08 2018
%Y Cf. A119017, A068425, A117721, A065987, A051480, A007514.
%Y Pi in base b: this sequence (b=2), A004602 (b=3), A004603 (b=4), A004604 (b=5), A004605 (b=6), A004606 (b=7), A006941 (b=8), A004608 (b=9), A000796 (b=10), A068436 (b=11), A068437 (b=12), A068438 (b=13), A068439 (b=14), A068440 (b=15), A062964 (b=16), A060707 (b=60).
%K nonn,base,cons,easy
%O 2,1
%A _N. J. A. Sloane_
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