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 A115624 Number of iterations of signature function required to get to [1] from partitions in Mathematica order. 3
 0, 1, 2, 1, 3, 2, 1, 3, 2, 4, 2, 1, 3, 3, 4, 4, 4, 2, 1, 3, 3, 4, 2, 3, 4, 2, 3, 4, 2, 1, 3, 3, 4, 3, 3, 4, 4, 4, 5, 4, 4, 4, 4, 2, 1, 3, 3, 4, 3, 3, 4, 2, 3, 4, 5, 4, 4, 3, 5, 5, 4, 2, 4, 4, 4, 2, 1, 3, 3, 4, 3, 3, 4, 3, 3, 4, 5, 4, 4, 3, 5, 5, 5, 4, 2, 5, 4, 4, 5, 5, 4, 4, 3, 4, 4, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The signature function takes a partition to the partition consisting of its repetition factors. LINKS Robert Price, Table of n, a(n) for n = 1..9295 (first 25 rows). EXAMPLE Partition 5 in Mathematica order is [2,1]. Applying the signature function to this repeatedly gives [2,1] -> [1^2] -> [2] -> [1], so a(5)=3. MATHEMATICA sig[x_] := Length@NestWhileList[Last@Transpose@Tally@# &, x, # != {1} &, 1] - 1; Table[sig /@ IntegerPartitions[n], {n, 8}]  // Flatten (* Robert Price, Jun 12 2020 *) CROSSREFS Cf. A115621, A113787, Sequence of first partitions with a(m)=n is A012257, with initial rows {1} and {2} in prepended. See A080577 for Mathematica partition order. Sequence in context: A088370 A328719 A113787 * A076291 A275015 A211189 Adjacent sequences:  A115621 A115622 A115623 * A115625 A115626 A115627 KEYWORD easy,nonn AUTHOR Franklin T. Adams-Watters, Jan 25 2006 STATUS approved

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Last modified July 26 06:53 EDT 2021. Contains 346294 sequences. (Running on oeis4.)