A088454 Decimal expansion of 6/(Catalan*Pi^2).

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, 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, 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

Offset: 0

Author

Eric W. Weisstein, Sep 30 2003

Keywords

• nonn
• cons
• easy

Comments

This is the probability that a randomly chosen Gaussian integer (e.g., -2 + 5i) is squarefree (Pegg, 2003). - Alonso del Arte, Dec 20 2013

The probability that two randomly selected Gaussian integers are relatively prime (Collins and Johnson, 1989). - Amiram Eldar, Nov 24 2023

Examples

			0.663700804613853460721431657617048691358...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• George E. Collins and Jeremy R. Johnson, The probability of relative primality of Gaussian integers, Symbolic and Algebraic Computation: International Symposium ISSAC'88 Rome, Italy, July 4-8, 1988 Proceedings, Springer Berlin Heidelberg, 1989, pp. 252-258.
• Ed Pegg Jr., The Moebius Function, 2003.
• Eric Weisstein's World of Mathematics, Gaussian Integer.
• Eric Weisstein's World of Mathematics, Relatively Prime.
• Eric Weisstein's World of Mathematics, Squarefree.

Crossrefs

Cf. A059956, A006752.

Programs

Magma

R:= RealField(100); 6/(Catalan(R)*Pi(R)^2); // G. C. Greubel, Aug 23 2018

Mathematica

RealDigits[(6/Pi^2)/Catalan, 10, 100][[1]] (* Alonso del Arte, Dec 20 2013 *)

PARI

6/(Catalan*Pi^2) \\ G. C. Greubel, Aug 23 2018