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%I #72 Mar 15 2024 23:39:50
%S 3,31,314,3141,31415,314159,3141592,31415926,314159265,3141592653,
%T 31415926535,314159265358,3141592653589,31415926535897,
%U 314159265358979,3141592653589793,31415926535897932,314159265358979323,3141592653589793238,31415926535897932384
%N a(n) is the integer whose decimal digits are the first n+1 decimal digits of Pi.
%C Number of collisions occurring in a system consisting of an infinitely massive, rigid wall at the origin, a ball with mass m stationary at position x1 > 0, and a ball with mass (10^2n)m at position x2 > x1 and rolling toward the origin, assuming perfectly elastic collisions and no friction. - _Richard Holmes_, Jun 17 2021
%C Wolfgang Haken (1977) conjectured that no term of this sequence is a perfect square, and estimated the probability that this conjecture is false to be smaller than 10^-9. - _Paolo Xausa_, Jul 15 2023
%D Martin Gardner, Fractal Music, Hypercards and More: Mathematical Recreations from Scientific American Magazine, W. H. Freemand and Company, New York, NY, 1992, pp. 274-275.
%H Paolo Xausa, <a href="/A011545/b011545.txt">Table of n, a(n) for n = 0..100</a>
%H G. Galperin, <a href="https://www.maths.tcd.ie/~lebed/Galperin.%20Playing%20pool%20with%20pi.pdf">Playing pool with π (the number π from a billiard point of view)</a>, Regular and Chaotic Dynamics, 8 (2003), 375-394.
%H Wolfgang Haken, <a href="https://doi.org/10.1002/jgt.3190010304">An attempt to understand the four color problem</a>, in Journal of Graph Theory, Vol. 1, Issue 3, 1977, pp. 193-206.
%H G. Sanderson, <a href="https://youtu.be/jsYwFizhncE">Why do colliding blocks compute pi?</a>, a 3Blue1Brown YouTube video, Jan 20 2019.
%F a(n) = floor(Pi*10^n).
%t s=RealDigits[Pi, 10, 30][[1]]; Table[FromDigits[Take[s, n]], {n, Length[s]}]
%t (* Or: *)
%t a[n_] := IntegerPart[Pi*10^n]; Table[a[n], {n, 0, 9}] (* _Peter Luschny_, Mar 15 2024 *)
%o (PARI) A011545(n)={localprec(n+3); Pi\10^-n} \\ _M. F. Hasler_, Mar 15 2024
%Y Cf. A000796 (decimal expansion of Pi), A089281, A078604, A089282, A089283, A089284, A089285, A089286, A089287, A089288, A089289, A046974, A089290.
%K nonn,base
%O 0,1
%A _N. J. A. Sloane_
%E Definition corrected by _M. F. Hasler_, Mar 15 2024
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