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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
Arturas Dubickas, Aivaras Novikas, Integer parts of powers of rational numbers, Math. Z. 251 (2005), 635-648, available from the first author's page.
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. A064628. - Tomohiro Yamada, Apr 23 2017
Sequence in context: A018120 A240200 A094979 * A309795 A017842 A157725
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 April 24 20:08 EDT 2024. Contains 371963 sequences. (Running on oeis4.)