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A064628
a(n) = floor((4/3)^n).
21
1, 1, 1, 2, 3, 4, 5, 7, 9, 13, 17, 23, 31, 42, 56, 74, 99, 133, 177, 236, 315, 420, 560, 747, 996, 1328, 1771, 2362, 3149, 4199, 5599, 7466, 9954, 13273, 17697, 23596, 31462, 41950, 55933, 74577, 99437, 132583, 176777, 235703, 314271, 419028, 558704
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
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.
Eric Weisstein's World of Mathematics, Power Floors.
Wikipedia, n-flake.
MAPLE
A064628:=n->floor(4^n/3^n); seq(A064628(n), n=0..30); # Wesley Ivan Hurt, Apr 19 2014
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
Cf. A046038, A070761, A070762, A067905 (Composites and Primes).
Sequence in context: A036802 A333265 A055167 * A188674 A320316 A236166
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