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A220395 A modified Engel expansion of log(2). 5
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, 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, 90, 294, 40, 2, 2, 32, 155, 8, 7, 12, 2, 2, 2, 2, 4, 6, 3, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A220393 for the definition of the modified Engel expansion of a positive real number. For further details see the Bala link.

LINKS

Table of n, a(n) for n=1..77.

P. Bala, A modified Engel expansion

S. Crowley, Integral transforms of the harmonic sawtooth map, the Riemann zeta function, fractal strings, and a finite reflection formula, arXiv:1210.5652 [math.NT]

Wikipedia, Engel Expansion

FORMULA

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))}.

Put P(n) = product {k = 1..n} a(k). Then we have the Egyptian fraction series expansion log(2) = sum {n = 1..inf} 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.

CROSSREFS

Cf. A059180, A220335, A220336, A220337, A220338, A220393, A220394, A220396, A220397, A220398.

Sequence in context: A073656 A047930 A073875 * A160099 A321336 A093098

Adjacent sequences:  A220392 A220393 A220394 * A220396 A220397 A220398

KEYWORD

nonn,easy

AUTHOR

Peter Bala, Dec 13 2012

STATUS

approved

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Last modified May 24 04:25 EDT 2019. Contains 323528 sequences. (Running on oeis4.)