A082913 Least k such that H(k) > 2^n, where H(k) is the harmonic number Sum_{i=1..k} 1/i.

2, 4, 31, 1674, 4989191, 44334502845080, 3500783582875029181027036603, 21827907538883637012326748457700300661358717434156476363

Offset

0,1

References

Julian Havil, Gamma, Exploring Euler's Constant, Princeton University Press, Princeton and Oxford, 2003, page 23.

Murray Schechter, Summation of divergent series by computer, Amer. Math. Monthly, 91:10 (1984), 629-632. See Table 1.

Links

Table of n, a(n) for n=0..7.

Formula

H(k) ~= log(k) + Euler's Gamma Constant (A001620) + 1/(2k).

a(n) = A002387(2^n). - Joerg Arndt, Jul 13 2015

Mathematica

f[n_] := Floor[Exp[n - EulerGamma] - 1/2] + 1; Table[ f[ 2^n], {n, 0, 7}]

Crossrefs

Cf. A002387, A001620.

Sequence in context: A087186 A051759 A051570 * A083205 A019542 A319223

Adjacent sequences: A082910 A082911 A082912 * A082914 A082915 A082916

Keyword

nonn

Author

Robert G. Wilson v, Apr 14 2003

Status

approved