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 A153810 Decimal expansion of 1 - gamma, where gamma is Euler's constant (or the Euler-Mascheroni constant). 3
 4, 2, 2, 7, 8, 4, 3, 3, 5, 0, 9, 8, 4, 6, 7, 1, 3, 9, 3, 9, 3, 4, 8, 7, 9, 0, 9, 9, 1, 7, 5, 9, 7, 5, 6, 8, 9, 5, 7, 8, 4, 0, 6, 6, 4, 0, 6, 0, 0, 7, 6, 4, 0, 1, 1, 9, 4, 2, 3, 2, 7, 6, 5, 1, 1, 5, 1, 3, 2, 2, 7, 3, 2, 2, 2, 3, 3, 5, 3, 2, 9, 0, 6, 3, 0, 5, 2, 9, 3, 6, 7, 0, 8, 2, 5, 3, 2, 5, 0, 4, 8, 5, 3, 6, 8 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Average fractional part of a random (large) integer when divided by all numbers up to it. The result remains true if primes or numbers from particular (fixed) congruence classes are used instead. The result is due to Vallée Poussin. - Charles R Greathouse IV, Apr 11 2012 Expected value of the fractional part of 1/x where x is chosen uniformly at random from (0, 1]. - Charles R Greathouse IV, Apr 11 2012 Value of digamma function psi(x) for x=2. - Stanislav Sykora, Apr 30 2012 The asymptotic evaluation of the counting function of A064052 ("jagged" numbers) is j(n) ~ log(2)*n - (1-gamma)*n/log(n) + ... - Jean-François Alcover, May 16 2014, after Steven Finch. Letting eta denote the Dirichlet eta function, and letting zeta denote the Riemann zeta function, we have that 1-gamma is equal to lim x -> infinity 2^x+(4/3)^x-zeta(2-eta(x)). - John M. Campbell, Jan 28 2016 REFERENCES Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, chapter 2.21, p. 166. LINKS G. C. Greubel, Table of n, a(n) for n = 0..2000 Friedrich Pillichshammer, Euler's constant and averages of fractional parts Charles Jean de la Vallée Poussin, Sur les valeurs moyennes de certaines fonctions arithmétiques, Annales de la société scientifique de Bruxelles 22 (1898), pp. 84-90. Wikipedia, Digamma function FORMULA Integral from 1 to infinity of {x}dx/x^2, where {x} is the fractional part of x. - Charles R Greathouse IV, Apr 11 2012 Also integral from 0 to infinity of x*log(x)*exp(-x) dx. Jean-François Alcover, Jun 17 2013 Sum_{n>=2} (Zeta(n)-1)/n. - Vaclav Kotesovec, Dec 11 2015 EXAMPLE 0.422784335... MATHEMATICA RealDigits[N[PolyGamma[2], 105]][[1]] (* Arkadiusz Wesolowski, Jan 10 2013 *) RealDigits[1 - EulerGamma, 10, 50][[1]] (* G. C. Greubel, Aug 29 2016 *) PROG (PARI) 1-Euler \\ Charles R Greathouse IV, Apr 11 2012 CROSSREFS Cf. A001620. Sequence in context: A270809 A087507 A020777 * A098134 A079191 A079184 Adjacent sequences:  A153807 A153808 A153809 * A153811 A153812 A153813 KEYWORD cons,nonn,nice AUTHOR Omar E. Pol, Jan 28 2009 EXTENSIONS More digits from R. J. Mathar, Feb 06 2009 STATUS approved

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Last modified November 16 15:26 EST 2018. Contains 317274 sequences. (Running on oeis4.)