A071315 Number of terms in the continued fraction of frac((3/2)^n).

1, 1, 3, 1, 4, 6, 5, 9, 7, 7, 4, 7, 12, 6, 9, 12, 9, 10, 9, 13, 18, 14, 12, 11, 12, 15, 16, 14, 10, 16, 23, 20, 28, 22, 17, 22, 23, 25, 30, 27, 25, 28, 30, 23, 30, 27, 25, 19, 17, 17, 22, 29, 32, 35, 35, 30, 32, 37, 36, 34, 36, 28, 39, 42, 44, 38, 36, 39, 38, 41, 46, 40, 32, 44

Offset: 1

Author

Paul D. Hanna, Jun 11 2002

Keywords

• nonn

Comments

What is the rate of growth of this sequence?

Numerically, it seems to be linear with coefficient around 0.58. [Charles R Greathouse IV, Jul 29 2011]

Examples

			a(3) = 3 since frac((3/2)^n) = [0;2,1,2] has 3 terms (2,1,2).
		

References

• S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 192-199.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Steven R. Finch, Powers of 3/2 Modulo One [From Steven Finch, Apr 20 2019]
• Steven R. Finch, Non-Ideal Waring's Problem [From Steven Finch, Apr 20 2019]
• Jeff Lagarias, 3x+1 Problem

Crossrefs

Cf. A002379.

Programs

PARI

a(n)=my(x=(3/2)^n);#contfrac(x-floor(x))-1 \\ Charles R Greathouse IV, Jul 29 2011