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.
%I A088453 #45 Aug 29 2025 07:03:26
%S A088453 8,3,1,9,0,7,3,7,2,5,8,0,7,0,7,4,6,8,6,8,3,1,2,6,2,7,8,8,2,1,5,3,0,7,
%T A088453 3,4,4,1,7,0,5,6,3,9,7,7,3,3,7,2,8,0,7,9,2,7,9,6,7,0,3,3,2,8,6,4,4,5,
%U A088453 7,8,7,9,1,7,2,3,4,7,9,8,8,8,2,1,3,6,5,6,6,8,9,8,9,9,6,5,3,0,4,0,9,8
%N A088453 Decimal expansion of 1/zeta(3).
%C A088453 This is the probability that three randomly chosen integers are relatively prime (see A018805). - Gary McGuire, Dec 13 2004
%C A088453 This is also the probability that a random integer is cubefree. - Eugene Salamin, Dec 13 2004
%C A088453 On the other hand, the probability that three randomly-chosen integers are pairwise relatively prime is given by A065473. - _Charles R Greathouse IV_, Nov 14 2011
%C A088453 This is also the 'probability' that a random algebraic number's denominator is equal to its leading coefficient, see Arno, Robinson, & Wheeler. - _Charles R Greathouse IV_, Nov 12 2014
%C A088453 This is the probability that a random point on a cubic lattice is visible from the origin, i.e., there is no other lattice point that lies on the line segment between this point and the origin. - _Amiram Eldar_, Jul 08 2020
%D A088453 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.6, p. 41.
%D A088453 David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987, p. 29.
%H A088453 Steven Arno, M. L. Robinson, and Ferell S. Wheeler, <a href="https://doi.org/10.1006/jnth.1996.0049">On denominators of algebraic numbers and integer polynomials</a>, Journal of Number Theory 57:2 (April 1996), pp. 292-302.
%H A088453 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RelativelyPrime.html">Relatively Prime</a>.
%F A088453 Equals 1/A002117.
%F A088453 From _Amiram Eldar_, Aug 20 2020: (Start)
%F A088453 Equals Sum_{k>=1} mu(k)/k^3, where mu is the Möbius function (A008683).
%F A088453 Equals Product_{p prime} (1 - 1/p^3). (End)
%e A088453 0.831907372580707468683126278821530734417...
%t A088453 RealDigits[1/Zeta[3],10,120][[1]] (* _Harvey P. Dale_, May 31 2019 *)
%o A088453 (Maxima) fpprec : 200$ bfloat( 1/zeta(3))$ bfloat(%); /* _Martin Ettl_, Oct 15 2012 */
%o A088453 (PARI) 1/zeta(3) \\ _Charles R Greathouse IV_, Nov 12 2014
%Y A088453 Cf. A002117, A008683.
%K A088453 nonn,cons,easy,changed
%O A088453 0,1
%A A088453 _Eric W. Weisstein_, Sep 30 2003
%E A088453 Entry revised by _N. J. A. Sloane_, Dec 16 2004