A185050 Least k such that G(k) > 3 - 1/2^n, where G(k) is the sum of the first k terms of the geometric series 1 + 2/3 + (2/3)^2 + ....

3, 5, 7, 8, 10, 12, 13, 15, 17, 19, 20, 22, 24, 25, 27, 29, 31, 32, 34, 36, 37, 39, 41, 43, 44, 46, 48, 49, 51, 53, 54, 56, 58, 60, 61, 63, 65, 66, 68, 70, 72, 73, 75, 77, 78, 80, 82, 84, 85, 87, 89, 90, 92, 94, 96, 97, 99, 101, 102, 104, 106, 107, 109, 111, 113

Offset

0,1

Comments

Many of terms in this sequence are that same as A186219(n+2) but not all.

References

Mohammad K. Azarian, Geometric Series, Problem 329, Mathematics and Computer Education, Vol. 30, No. 1, Winter 1996, p. 101. Solution published in Vol. 31, No. 2, Spring 1997, pp. 196-197.

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Eric Weisstein's World of Mathematics, Geometric Series

Example

a(1) = 5 because 1 + 2/3 + (2/3)^2 + (2/3)^3 + (2/3)^4 > 3 - 1/2.

Mathematica

lst = {}; n = s = 0; Do[s = s + (2/3)^k; If[s > 3 - 1/2^n, AppendTo[lst, k + 1]; n++], {k, 0, 112}]; lst

Crossrefs

Sequence in context: A186315 A285074 A186219 * A083034 A213908 A247514

Adjacent sequences: A185047 A185048 A185049 * A185051 A185052 A185053

Keyword

nonn

Author

Arkadiusz Wesolowski, Dec 25 2012

Status

approved