# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a064628 Showing 1-1 of 1 %I A064628 #38 Oct 14 2024 02:55:18 %S A064628 1,1,1,2,3,4,5,7,9,13,17,23,31,42,56,74,99,133,177,236,315,420,560, %T A064628 747,996,1328,1771,2362,3149,4199,5599,7466,9954,13273,17697,23596, %U A064628 31462,41950,55933,74577,99437,132583,176777,235703,314271,419028,558704 %N A064628 a(n) = floor((4/3)^n). %C A064628 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 %C A064628 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 %D A064628 R. K. Guy, Unsolved Problems in Number Theory, E19. %H A064628 Harry J. Smith, Table of n, a(n) for n=0,...,400 %H A064628 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. %H A064628 W. Forman and H. N. Shapiro, An arithmetic property of certain rational powers, Comm. Pure. Appl. Math. 20 (1967), 561-573. %H A064628 Kival Ngaokrajang, Illustration of hexaflake for n = 0..3. %H A064628 Eric Weisstein's World of Mathematics, Power Floors. %H A064628 Wikipedia, n-flake. %p A064628 A064628:=n->floor(4^n/3^n); seq(A064628(n), n=0..30); # _Wesley Ivan Hurt_, Apr 19 2014 %t A064628 Table[Floor[(4/3)^n], {n, 0, 30}] (* _Robert G. Wilson v_ *) %o A064628 (PARI) { f=t=1; for (n=0, 400, write("b064628.txt", n, " ", f\t); f*=4; t*=3 ) } \\ _Harry J. Smith_, Sep 20 2009 %o A064628 (Sage) def A064628(n): return floor((4/3)^n) %o A064628 [A064628(n) for n in range(0, 46)] # _Stefano Spezia_, Oct 13 2024 %Y A064628 Cf. A002379, A002380, A060692. %Y A064628 Cf. A094969 - A094500. %Y A064628 Cf. A046038, A070761, A070762, A067905 (Composites and Primes). %K A064628 nonn,easy %O A064628 0,4 %A A064628 _Labos Elemer_, Oct 01 2001 %E A064628 More terms from _Robert G. Wilson v_, May 26 2004 %E A064628 OFFSET changed from 1 to 0 by _Harry J. Smith_, Sep 20 2009 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE