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HTTP/2 200 date: Fri, 16 Jan 2026 04:57:43 GMT content-type: text/html; charset=utf-8 cache-control: private, no-store last-modified: Mon, 03 Nov 2025 07:53:00 GMT vary: * cf-cache-status: DYNAMIC nel: {"report_to":"cf-nel","success_fraction":0.0,"max_age":604800} report-to: {"group":"cf-nel","max_age":604800,"endpoints":[{"url":"https://a.nel.cloudflare.com/report/v4?s=R80rXbzRyQmRWsgMIJUhk9tNQu1qm0cdh5vS1YcHemxhxQd7DxfwTiLXiOIckeyKH8gHT6tHyDVxZhuTzk06WzHeviVNAsBZ"}]} content-encoding: gzip server: cloudflare cf-ray: 9beb089c9bf2dab3-BOM alt-svc: h3=":443"; ma=86400 A088454 - OEIS

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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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

0,1

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

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.

Michael Penn, How often (Gaussian) integers are relatively prime, YouTube video, 2025.

Eric Weisstein's World of Mathematics, Gaussian Integer.

Eric Weisstein's World of Mathematics, Relatively Prime.

Eric Weisstein's World of Mathematics, Squarefree.

EXAMPLE

0.663700804613853460721431657617048691358...

MATHEMATICA

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

PROG

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

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