cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A065480 Decimal expansion of Product_{p prime} (1 - 1/(p^2+p-1)).

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%I A065480 #31 Mar 14 2021 05:14:29
%S A065480 6,6,9,5,8,0,2,9,0,5,3,9,0,6,2,3,6,7,6,3,5,0,2,5,6,9,5,6,1,2,4,3,4,2,
%T A065480 2,7,2,1,7,3,3,9,8,2,5,4,1,6,2,3,3,0,2,5,6,2,4,6,5,4,6,2,6,3,3,0,9,8,
%U A065480 3,6,6,1,9,9,5,4,7,2,4,5,7,1,4,5,7,5,6,6,2,6,0,3,8,6,9,6,3,8
%N A065480 Decimal expansion of Product_{p prime} (1 - 1/(p^2+p-1)).
%C A065480 The probability that two numbers are coprime given that they are both coprime to a randomly chosen third number. - _Luke Palmer_, Apr 27 2019
%H A065480 G. Niklasch, <a href="/A001692/a001692.html">Some number theoretical constants: 1000-digit values</a>. [Cached copy]
%F A065480 Equals A065473*zeta(2)/A065463. - _Luke Palmer_, Apr 27 2019
%e A065480 0.6695802905390623676350256956124342...
%t A065480 digits = 98; Exp[NSum[(1/2)*(-2 + (-2)^n - ((1/2)*(-1 - Sqrt[5]))^n*(-1 + Sqrt[5]) + ((1/2)*(-1 + Sqrt[5]))^n*(1 + Sqrt[5]))*PrimeZetaP[n - 1]/(n - 1), {n, 3, Infinity}, WorkingPrecision -> 4 digits, Method -> "AlternatingSigns"]] // RealDigits[#, 10, digits]& // First (* _Jean-François Alcover_, Apr 18 2016 *)
%o A065480 (PARI) prodeulerrat(1 - 1/(p^2+p-1)) \\ _Amiram Eldar_, Mar 14 2021
%Y A065480 Cf. A065592, A078081.
%Y A065480 Cf. A013661, A065463, A065473.
%K A065480 cons,nonn
%O A065480 0,1
%A A065480 _N. J. A. Sloane_, Nov 19 2001