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%I #13 Jul 26 2021 01:48:07
%S 2,3,8,6,2,4,93,60,2,2,2,2,3,12,10,2,2,14,52,6,5,8,2,2,5,8,2,2,3,4,14,
%T 273,40,2,3,4,4,12,27,16,14,26,4,6,4,6,2,3,12,10,4,6,14,65,12,8,6,2,7,
%U 90,294,40,2,2,32,155,8,7,12,2,2,2,2,4,6,3,10
%N A modified Engel expansion of log(2).
%C See A220393 for the definition of the modified Engel expansion of a positive real number. For further details see the Bala link.
%H Peter Bala, <a href="/A220393/a220393.pdf">A modified Engel expansion</a>
%H S. Crowley, <a href="http://arxiv.org/abs/1210.5652">Integral transforms of the harmonic sawtooth map, the Riemann zeta function, fractal strings, and a finite reflection formula</a>, arXiv:1210.5652 [math.NT], 2012-2020.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Engel_expansion">Engel Expansion</a>
%F Let h(x) = x*(floor(1/x) + (floor(1/x))^2) - floor(1/x). Let x = log(2). Then a(1) = 1 + floor(1/x) and, for n >= 1, a(n+1) = floor(1/h^(n-1)(x))*(1 + floor(1/h^(n)(x))).
%F Put P(n) = Product_{k = 1..n} a(k). Then we have the Egyptian fraction series expansion log(2) = Sum_{n>=1} 1/P(n) = 1/2 + 1/(2*3) + 1/(2*3*8) + 1/(2*3*8*6) + 1/(2*3*8*6*2) + .... The error made in truncating this series to n terms is less than the n-th term.
%Y Cf. A059180, A220335, A220336, A220337, A220338, A220393, A220394, A220396, A220397, A220398.
%K nonn,easy
%O 1,1
%A _Peter Bala_, Dec 13 2012
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