A065565 a(n) = floor((5/4)^n).

1, 1, 1, 1, 2, 3, 3, 4, 5, 7, 9, 11, 14, 18, 22, 28, 35, 44, 55, 69, 86, 108, 135, 169, 211, 264, 330, 413, 516, 646, 807, 1009, 1262, 1577, 1972, 2465, 3081, 3851, 4814, 6018, 7523, 9403, 11754, 14693, 18367, 22958, 28698, 35873, 44841, 56051, 70064, 87581

Offset: 0

Author

Benoit Cloitre, Nov 30 2001

Keywords

• nonn

Comments

a(n) is also the curvature (rounded down) of the circle inscribed in the n-th 3:4:5 triangle arranged in a spiral as shown in the illustration in the links section. - Kival Ngaokrajang, Aug 21 2013

By the result of Dubickas and Novikas, a(n) is divisible by at least one of 2, 3, 7, 11, 13 infinitely often, so that a(n) is composite infinitely often. - Tomohiro Yamada, Apr 23 2017

Links

• Harry J. Smith, Table of n, a(n) for n = 0..400
• Arturas Dubickas, Aivaras Novikas, Integer parts of powers of rational numbers, Math. Z. 251 (2005), 635-648, available from the first author's page.
• Kival Ngaokrajang, Illustration of some initial terms.

Crossrefs

Cf. A002379, A094969-A094500.

Cf. A064628. - Tomohiro Yamada, Apr 23 2017

Programs

Mathematica

Table[ Floor[(5/4)^n], {n, 0, 41}] (* Robert G. Wilson v, May 26 2004 *)

PARI

a(n) = floor((5/4)^n) \\ Harry J. Smith, Oct 22 2009

Extensions

Edited by N. J. A. Sloane at the suggestion of Stefan Steinerberger, Jun 20 2007

Offset changed from 1 to 0 by Harry J. Smith, Oct 22 2009