A248562 - OEIS

A248562

Least k such that log(3/2) - sum{1/(h*3^h), h = 1..k} < 1/6^n.

1, 2, 3, 5, 6, 8, 9, 11, 12, 14, 15, 17, 18, 20, 22, 23, 25, 26, 28, 29, 31, 33, 34, 36, 37, 39, 41, 42, 44, 45, 47, 49, 50, 52, 53, 55, 57, 58, 60, 61, 63, 65, 66, 68, 69, 71, 73, 74, 76, 77, 79, 81, 82, 84, 86, 87, 89, 90, 92, 94, 95, 97, 98, 100, 102, 103

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OFFSET

1,2

COMMENTS

This sequence provides insight into the manner of convergence of sum{1/(h*3^h), h = 1..k} to log(3/2). Since a(n+1) - a(n) is in {1,2} for n >= 1, the sequences A248563 and A248564 partition the positive integers.

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 s(n) = log(3/2) - sum{1/(h*3^h), h = 1..n}. Approximations follow:

n ... s(n) ........ 1/6^n

1 ... 0.0721318 ... 0.166667

2 ... 0.0165762 ... 0.0277777

3 ... 0.0042305 ... 0.0046296

4 ... 0.0011441 ... 0.0007716

5 ... 0.0003210 ... 0.0001286