This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A064628 #39 Feb 16 2025 08:32:45
%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, <a href="/A064628/b064628.txt">Table of n, a(n) for n=0,...,400</a>
%H A064628 Arturas Dubickas and Aivaras Novikas, <a href="https://doi.org/10.1007/s00209-005-0827-4">Integer parts of powers of rational numbers</a>, Math. Z. 251 (2005), 635--648, available from <a href="http://www.mif.vu.lt/~dubickas/files/dvifai/suaivaru.pdf">the first author's page</a>.
%H A064628 W. Forman and H. N. Shapiro, <a href="https://doi.org/10.1002/cpa.3160200305">An arithmetic property of certain rational powers</a>, Comm. Pure. Appl. Math. 20 (1967), 561-573.
%H A064628 Kival Ngaokrajang, <a href="/A064628/a064628.pdf">Illustration of hexaflake for n = 0..3</a>.
%H A064628 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PowerFloors.html">Power Floors</a>.
%H A064628 Wikipedia, <a href="http://en.wikipedia.org/wiki/N-flake">n-flake</a>.
%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