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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 (list; graph; refs; listen; history; text; internal format)
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), 635-648, 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, A094969-A094500.

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

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Last modified March 24 12:14 EDT 2019. Contains 321448 sequences. (Running on oeis4.)