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A247983 Least number k such that log(2) - sum{1/(h*2^h), h=1..k} < 1/2^n. 2
1, 1, 2, 3, 3, 4, 5, 6, 7, 7, 8, 9, 10, 11, 12, 13, 14, 15, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

It appears that a(n+1) - a(n) if and only if n is in A083706(n), for n >= 1.

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 15.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000

EXAMPLE

Let w(n) = log(2) - sum{1/(h*2^h), h=1..n}.  Approximations are shown here:

n .... w(n)  ...... 1/2^n

1 ... 0.193147 .... 0.5

2 ... 0.0681472 ... 0.25

3 ... 0.0264805 ... 0.125

4 ... 0.0108555 ... 0.0625

5 ... 0.0046055 ... 0. 03125

a(4) = 3 because w(3) < 1/2^4 < w(2).

MATHEMATICA

z = 200; s[k_] := s[k] = Sum[1/(h*2^h), {h, 1, k}];

N[Table[Log[2] - s[n], {n, 1, z/8}]]

f[n_] := f[n] = Select[Range[z], Log[2] - s[#] < 1/2^n &, 1];

u = Flatten[Table[f[n], {n, 1, z}]]   (* A247983 *)

CROSSREFS

Cf. A083706, A247968.

Sequence in context: A138467 A208746 A230490 * A127036 A108789 A091960

Adjacent sequences:  A247980 A247981 A247982 * A247984 A247985 A247986

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Sep 28 2014

STATUS

approved

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Last modified September 23 18:00 EDT 2021. Contains 347617 sequences. (Running on oeis4.)