cp's OEIS Frontend

A356624 After n iterations of the "Square Multiscale" substitution, the largest tiles have side length 3^t / 5^f; a(n) = t (A356625 gives corresponding f's).

%I A356624 #14 Aug 21 2022 06:15:11
%S A356624 0,1,2,3,0,4,1,5,2,6,3,0,7,4,1,8,5,2,9,6,3,0,10,7,4,1,11,8,5,2,12,9,6,
%T A356624 3,0,13,10,7,4,1,14,11,8,5,2,15,12,9,6,3,0,16,13,10,7,4,1,17,14,11,8,
%U A356624 5,2,18,15,12,9,6,3,0,19,16,13,10,7,4,1,20,17
%N A356624 After n iterations of the "Square Multiscale" substitution, the largest tiles have side length 3^t / 5^f; a(n) = t (A356625 gives corresponding f's).
%C A356624 See A329919 for further details about the "Square Multiscale" substitution.
%H A356624 Rémy Sigrist, <a href="/A356624/b356624.txt">Table of n, a(n) for n = 0..10000</a>
%H A356624 Yotam Smilansky and Yaar Solomon, <a href="https://arxiv.org/abs/2003.11735">Multiscale Substitution Tilings</a>, arXiv:2003.11735 [math.DS], 2020.
%F A356624 5^A356625(n) >= 3^a(n).
%e A356624 The first terms, alongside the corresponding side lengths, are:
%e A356624   n   a(n)  Side length
%e A356624   --  ----  -----------
%e A356624    0     0            1
%e A356624    1     1          3/5
%e A356624    2     2         9/25
%e A356624    3     3       27/125
%e A356624    4     0          1/5
%e A356624    5     4       81/625
%e A356624    6     1         3/25
%e A356624    7     5     243/3125
%e A356624    8     2        9/125
%e A356624    9     6    729/15625
%e A356624   10     3       27/625
%o A356624 (PARI) { sc = [1]; for (n=0, 78, s = vecmax(sc); print1 (valuation(s,3)", "); sc = setunion(setminus(sc,[s]), Set([3*s/5, s/5]))) }
%Y A356624 Cf. A022336, A329919, A354535, A356625.
%K A356624 nonn
%O A356624 0,3
%A A356624 _Rémy Sigrist_, Aug 17 2022