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A356625
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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).
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2
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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
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OFFSET
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0,3
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COMMENTS
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See A329919 for further details about the "Square Multiscale" substitution.
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LINKS
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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.
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FORMULA
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5^a(n) >= 3^A356624(n).
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EXAMPLE
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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
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PROG
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(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]))) }
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CROSSREFS
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Cf. A022337, A329919, A354535, A356624.
Sequence in context: A118276 A023123 A023131 * A026276 A152201 A265579
Adjacent sequences: A356622 A356623 A356624 * A356626 A356627 A356628
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KEYWORD
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nonn
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AUTHOR
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Rémy Sigrist, Aug 17 2022
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STATUS
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approved
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