A071316 Sum of terms of continued fraction expansion of frac((3/2)^n).

2, 4, 5, 16, 10, 10, 17, 13, 20, 74, 113, 32, 25, 76, 55, 31, 44, 86, 74, 46, 42, 100, 402, 115, 63, 71, 104, 143, 489, 346, 96, 78, 68, 87, 167, 196, 116, 95, 76, 123, 109, 108, 141, 176, 141, 133, 260, 1038, 4748, 5731, 1162, 285, 189, 248, 478, 399, 163, 154

Offset: 1

Author

Paul D. Hanna, Jun 11 2002

Keywords

• nonn

Comments

What is the rate of growth of this sequence?

Examples

			a(3) = 5 since frac((3/2)^3) = [0;2,1,2] and a(3) = 2 + 1 + 2.
		

References

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000
• 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, A071315.

Programs

PARI

a(n) = {cf = contfrac((3/2)^n); return (sum(i=2, #cf, cf[i]));} \\ Michel Marcus, Aug 01 2013

Extensions

Name corrected by Sean A. Irvine, Jul 11 2024