A248636 - OEIS

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A248636

Least k such that 33/8- sum{(h^3)/3^h, h = 1..k} < 1/4^n.

7, 9, 10, 12, 13, 15, 17, 18, 19, 21, 22, 24, 25, 27, 28, 29, 31, 32, 34, 35, 36, 38, 39, 40, 42, 43, 44, 46, 47, 48, 50, 51, 52, 54, 55, 56, 58, 59, 60, 62, 63, 64, 66, 67, 68, 70, 71, 72, 73, 75, 76, 77, 79, 80, 81, 83, 84, 85, 87, 88, 89, 90, 92, 93, 94

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OFFSET

1,1

COMMENTS

This sequence provides insight into the manner of convergence of sum{(h^3)/3^h, h = 1..k} to 33/8. The difference sequence of A248636 entirely of 1s and 2s, so that A248637 and A248638 partition the positive integers.

LINKS

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

EXAMPLE

Let s(n) = 33/8- sum{(h^3)/3^h, h = 1..n}. Approximations follow:

n ... s(n) ........ 1/4^n

1 ... 3.79167 ... 0.250000

2 ... 2.90278 ... 0.062500

3 ... 1.90278 ... 0.015625

4 ... 1.11265 ... 0.003906

5 ... 0.59825 ... 0.000976

6 ... 0.30195 ... 0.000244

7 ... 0.14511 ... 0.000061