A356625 - OEIS

%I #13 Aug 21 2022 06:15:28

%S 0,1,2,3,1,4,2,5,3,6,4,2,7,5,3,8,6,4,9,7,5,3,10,8,6,4,11,9,7,5,12,10,

%T 8,6,4,13,11,9,7,5,14,12,10,8,6,15,13,11,9,7,5,16,14,12,10,8,6,17,15,

%U 13,11,9,7,18,16,14,12,10,8,6,19,17,15,13,11,9,7

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

%C See A329919 for further details about the "Square Multiscale" substitution.

%H Rémy Sigrist, <a href="/A356625/b356625.txt">Table of n, a(n) for n = 0..10000</a>

%H Yotam Smilansky and Yaar Solomon, <a href="https://arxiv.org/abs/2003.11735">Multiscale Substitution Tilings</a>, arXiv:2003.11735 [math.DS], 2020.

%F 5^a(n) >= 3^A356624(n).

%e The first terms, alongside the corresponding side lengths, are:

%e   n   a(n)  Side length

%e   --  ----  -----------

%e    0     0            1

%e    1     1          3/5

%e    2     2         9/25

%e    3     3       27/125

%e    4     1          1/5

%e    5     4       81/625

%e    6     2         3/25

%e    7     5     243/3125

%e    8     3        9/125

%e    9     6    729/15625

%e   10     4       27/625

%o (PARI) { sc = [1]; for (n=0, 76, s = vecmax(sc); print1 (-valuation(s,5)", "); sc = setunion(setminus(sc,[s]), Set([3*s/5, s/5]))) }

%Y Cf. A022337, A329919, A354535, A356624.

%K nonn

%O 0,3

%A _Rémy Sigrist_, Aug 17 2022