

A065565


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


4



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
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OFFSET

0,5


COMMENTS

a(n) is also the number of the circle curvature (rounded down) inscribing in 3:4:5 triangle arranged as spiral form. See illustration in links.  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), 635648, available from the first author's page.
Kival Ngaokrajang, Illustration of some initial terms


MATHEMATICA

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


PROG

(PARI) for (n=0, 400, write("b065565.txt", n, " ", floor((5/4)^n)) ) \\ Harry J. Smith, Oct 22 2009


CROSSREFS

Cf. A002379, A094969A094500.
Cf. A064628.  Tomohiro Yamada, Apr 23 2017
Sequence in context: A018120 A240200 A094979 * A017842 A157725 A238394
Adjacent sequences: A065562 A065563 A065564 * A065566 A065567 A065568


KEYWORD

nonn


AUTHOR

Benoit Cloitre, Nov 30 2001


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


STATUS

approved



