OFFSET
0,4
COMMENTS
a(n) is the perimeter of a hexaflake (rounded down) after n iterations. The total number of holes = A000420(n) - 1. The total number of irregular polygon holes = A000420(n-1) - 1. The total number of triangle holes = 6*A000420(n-1). - Kival Ngaokrajang, Apr 18 2014
a(n) is composite infinitely often (Forman and Shapiro). More exactly, a(n) is divisible by at least one of 2, 3, 5 infinitely often (Dubickas and Novikas). - Tomohiro Yamada, Apr 15 2017
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, E19.
LINKS
Harry J. Smith, Table of n, a(n) for n=0,...,400
Arturas Dubickas and Aivaras Novikas, Integer parts of powers of rational numbers, Math. Z. 251 (2005), 635--648, available from the first author's page.
W. Forman and H. N. Shapiro, An arithmetic property of certain rational powers, Comm. Pure. Appl. Math. 20 (1967), 561-573.
Kival Ngaokrajang, Illustration of hexaflake for n = 0..3.
Eric Weisstein's World of Mathematics, Power Floors.
Wikipedia, n-flake.
MAPLE
MATHEMATICA
Table[Floor[(4/3)^n], {n, 0, 30}] (* Robert G. Wilson v *)
PROG
(PARI) { f=t=1; for (n=0, 400, write("b064628.txt", n, " ", f\t); f*=4; t*=3 ) } \\ Harry J. Smith, Sep 20 2009
(Sage) def A064628(n): return floor((4/3)^n)
[A064628(n) for n in range(0, 46)] # Stefano Spezia, Oct 13 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Labos Elemer, Oct 01 2001
EXTENSIONS
More terms from Robert G. Wilson v, May 26 2004
OFFSET changed from 1 to 0 by Harry J. Smith, Sep 20 2009
STATUS
approved