

A064628


Floor(4^n / 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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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(n1)  1. The total number of triangle holes = 6*A000420(n1).  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, Aivaras Novikas, Integer parts of powers of rational numbers, Math. Z. 251 (2005), 635648, 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), 561573.
Kival Ngaokrajang, Illustration of hexaflake for n = 0..3
Eric Weisstein's World of Mathematics, Power Floors
Wikipedia, nflake


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


CROSSREFS

Cf. A002379, A002380, A060692.
Cf. A094969  A094500.
Cf. A046038, A070761, A070762, A067905 (Composites and Primes).
Sequence in context: A036802 A333265 A055167 * A188674 A320316 A236166
Adjacent sequences: A064625 A064626 A064627 * A064629 A064630 A064631


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



