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 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). 2
 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 (list; graph; refs; listen; history; text; internal format)
 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: A118276 A023123 A023131 * A026276 A152201 A265579 Adjacent sequences: A356622 A356623 A356624 * A356626 A356627 A356628 KEYWORD nonn AUTHOR Rémy Sigrist, Aug 17 2022 STATUS approved

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Last modified March 25 03:37 EDT 2023. Contains 361511 sequences. (Running on oeis4.)