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 A113787 Number of iterations of signature function required to get to [1] from partitions in Abramowitz and Stegun order. 3
 0, 1, 2, 1, 3, 2, 1, 3, 2, 4, 2, 1, 3, 3, 4, 4, 4, 2, 1, 3, 3, 2, 4, 3, 2, 4, 3, 4, 2, 1, 3, 3, 3, 4, 3, 4, 4, 4, 5, 4, 4, 4, 4, 2, 1, 3, 3, 3, 2, 4, 3, 3, 4, 4, 4, 5, 3, 5, 2, 4, 5, 4, 4, 4, 4, 2, 1, 3, 3, 3, 3, 4, 3, 3, 4, 4, 3, 2, 4, 5, 5, 5, 5, 4, 4, 5, 4, 5, 4, 4, 5, 3, 4, 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). M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. EXAMPLE Partition 5 in A&S order is [1,2]. Applying the signature function to this repeatedly gives [1,2] -> [1^2] -> [2] -> [1], so a(5)=3. MATHEMATICA sig[x_] := Length@NestWhileList[Last@Transpose@Tally@# &, x, # != {1} &, 1] - 1; Table[sig /@ Sort[Reverse /@ IntegerPartitions[n]], {n, 9}]  // Flatten (* Robert Price, Jun 12 2020 *) CROSSREFS Cf. A115621, A115624, Sequence of first partitions with a(m)=n is A012257, with initial rows {1} and {2} in prepended. See A036036 for A&S partitions. Sequence in context: A256440 A088370 A328719 * A115624 A076291 A275015 Adjacent sequences:  A113784 A113785 A113786 * A113788 A113789 A113790 KEYWORD easy,nonn AUTHOR Franklin T. Adams-Watters, Jan 20 2006 STATUS approved

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Last modified July 24 03:29 EDT 2021. Contains 346273 sequences. (Running on oeis4.)