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 A217739 Decimal expansion of 8/Pi^2. 7
 8, 1, 0, 5, 6, 9, 4, 6, 9, 1, 3, 8, 7, 0, 2, 1, 7, 1, 5, 5, 1, 0, 3, 5, 7, 0, 5, 6, 7, 7, 8, 2, 1, 1, 1, 1, 2, 3, 4, 8, 7, 0, 1, 9, 7, 3, 7, 7, 9, 7, 2, 3, 9, 0, 7, 6, 4, 8, 7, 2, 2, 5, 5, 1, 5, 3, 3, 8, 4, 9, 6, 7, 6, 9, 7, 8, 8, 3, 5, 2, 9, 5, 2, 9, 6, 7, 4, 1, 9, 1, 4, 0, 4, 9, 7, 4, 7 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS This is the probability that a randomly chosen singly even number is squarefree. (The probability that any randomly chosen integer is squarefree is 6/Pi^2). This number also arises in the study of the Fourier series for a triangle wave. By Equation 6 given by Weisstein, this number is b_1, since b_n = 8/(Pi^2 n^2) for odd n. Springer labels this a_1. This is also the probability that the greatest common divisor of two randomly chosen positive integers will be a power of 2. Generally, the probability that the greatest common divisor of two random integers will be a power of p, a prime, is (6/Pi^2)/(1-1/p^2). Here we are considering the integer 1 to be a power of p. - Geoffrey Critzer, Jan 13 2015 The probability that two randomly chosen odd numbers will be coprime (Nymann, 1975). - Amiram Eldar, Aug 07 2020 LINKS Table of n, a(n) for n=0..96. J. E. Nymann, On the probability that k positive integers are relatively prime II, Journal of Number Theory, Vol. 7, No. 4 (1975), pp. 406-412. Matt Springer, Sunday Function, Built on Facts, Aug 16 2009, from ScienceBlogs. Eric Weisstein's World of Mathematics, Triangle Wave. Index entries for transcendental numbers FORMULA Equals -Sum_{k>=1} mu(2*k)/k^2, where mu is the Möbius function (A008683). - Amiram Eldar, Aug 20 2020 Equals Product_{k>=2} (1-1/k^2)^((-1)^k). - Amiram Eldar, Apr 09 2022 EXAMPLE 0.810569469138702171551... MATHEMATICA RealDigits[8/Pi^2, 10, 108] CROSSREFS Cf. A008683, A059956, A092742, A111003 (reciprocal). Sequence in context: A214097 A357468 A194732 * A110544 A320084 A153855 Adjacent sequences: A217736 A217737 A217738 * A217740 A217741 A217742 KEYWORD cons,nonn,easy AUTHOR Alonso del Arte, Mar 22 2013 STATUS approved

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Last modified April 20 09:59 EDT 2024. Contains 371807 sequences. (Running on oeis4.)