A356625 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).

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

Offset

0,3

Comments

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

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Yotam Smilansky and Yaar Solomon, Multiscale Substitution Tilings, arXiv:2003.11735 [math.DS], 2020.

Formula

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

Example

The first terms, alongside the corresponding side lengths, are:
  n   a(n)  Side length
  --  ----  -----------
   0     0            1
   1     1          3/5
   2     2         9/25
   3     3       27/125
   4     1          1/5
   5     4       81/625
   6     2         3/25
   7     5     243/3125
   8     3        9/125
   9     6    729/15625
  10     4       27/625

Prog

(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]))) }

Crossrefs

Cf. A022337, A329919, A354535, A356624.

Sequence in context: A023123 A023131 A375559 * A026276 A152201 A265579

Adjacent sequences: A356622 A356623 A356624 * A356626 A356627 A356628

Keyword

nonn

Author

Rémy Sigrist, Aug 17 2022

Status

approved