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%I #19 Nov 24 2023 09:00:24
%S 6,6,3,7,0,0,8,0,4,6,1,3,8,5,3,4,6,0,7,2,1,4,3,1,6,5,7,6,1,7,0,4,8,6,
%T 9,1,3,5,8,3,9,5,7,9,6,7,7,4,8,0,8,3,8,7,2,0,6,2,0,0,9,9,0,2,8,6,6,1,
%U 3,0,2,3,1,0,1,9,6,6,4,7,7,5,0,3,3,2,2,0,4,1,0,4,6,0,3,6,6,3,9,5,0,7
%N Decimal expansion of 6/(Catalan*Pi^2).
%C This is the probability that a randomly chosen Gaussian integer (e.g., -2 + 5i) is squarefree (Pegg, 2003). - _Alonso del Arte_, Dec 20 2013
%C The probability that two randomly selected Gaussian integers are relatively prime (Collins and Johnson, 1989). - _Amiram Eldar_, Nov 24 2023
%H G. C. Greubel, <a href="/A088454/b088454.txt">Table of n, a(n) for n = 0..10000</a>
%H George E. Collins and Jeremy R. Johnson, <a href="https://doi.org/10.1007/3-540-51084-2_23">The probability of relative primality of Gaussian integers</a>, Symbolic and Algebraic Computation: International Symposium ISSAC'88 Rome, Italy, July 4-8, 1988 Proceedings, Springer Berlin Heidelberg, 1989, pp. 252-258.
%H Ed Pegg Jr., <a href="http://www.mathpuzzle.com/MAA/02-Mobius%20Function/mathgames_11_03_03.html">The Moebius Function</a>, 2003.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GaussianInteger.html">Gaussian Integer</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RelativelyPrime.html">Relatively Prime</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Squarefree.html">Squarefree</a>.
%e 0.663700804613853460721431657617048691358...
%t RealDigits[(6/Pi^2)/Catalan, 10, 100][[1]] (* _Alonso del Arte_, Dec 20 2013 *)
%o (PARI) 6/(Catalan*Pi^2) \\ _G. C. Greubel_, Aug 23 2018
%o (Magma) R:= RealField(100); 6/(Catalan(R)*Pi(R)^2); // _G. C. Greubel_, Aug 23 2018
%Y Cf. A059956, A006752.
%K nonn,cons,easy
%O 0,1
%A _Eric W. Weisstein_, Sep 30 2003
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