

A246746


Decimal expansion of 'rho', an auxiliary constant associated with the asymptotic number of values of the Euler totient function less than a given number.


5



5, 4, 2, 5, 9, 8, 5, 8, 6, 0, 9, 8, 4, 7, 1, 0, 2, 1, 9, 5, 9, 3, 8, 4, 5, 9, 5, 7, 7, 9, 4, 6, 9, 4, 2, 6, 7, 7, 9, 5, 0, 4, 6, 1, 6, 1, 9, 5, 3, 9, 2, 4, 6, 9, 6, 6, 5, 1, 5, 7, 8, 1, 0, 3, 4, 7, 0, 8, 9, 3, 1, 8, 9, 4, 7, 6, 4, 5, 6, 2, 2, 3, 2, 9, 5, 9, 3, 7, 4, 7, 4, 5, 1, 3, 4, 8, 9, 1, 0, 9, 3
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OFFSET

0,1


LINKS

Table of n, a(n) for n=0..100.
Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 16.
Steven R. Finch, Errata and Addenda to Mathematical Constants, January 22, 2016. [Cached copy, with permission of the author]
Kevin Ford, The distribution of Totients


FORMULA

Rho is the unique solution on [0,1) of the equation F(rho)=1, where F(x) = sum_{k >= 1} ((k+1)*log(k+1)  k*log(k)  1)*x^k.


EXAMPLE

0.54259858609847102195938459577946942677950461619539246966515781...


MATHEMATICA

digits = 101; F[x_?NumericQ] := NSum[((k + 1)*Log[k + 1]  k*Log[k]  1)*x^k, {k, 1, Infinity}, WorkingPrecision > digits + 10, NSumTerms > 1000]; rho = x /. FindRoot[F[x] == 1, {x, 5/10, 6/10}, WorkingPrecision > digits + 10]; RealDigits[rho, 10, digits] // First


CROSSREFS

Sequence in context: A213205 A094778 A260849 * A180131 A257972 A222307
Adjacent sequences: A246743 A246744 A246745 * A246747 A246748 A246749


KEYWORD

nonn,cons


AUTHOR

JeanFrançois Alcover, Sep 02 2014


STATUS

approved



