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Search: id:A113787
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| A113787 |
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Number of iterations of signature function required to get to [1] from partitions in Abramowitz and Stegun order. |
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+0
3
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| 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; listen)
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OFFSET
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1,3
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COMMENT
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The signature function takes a partition to the partition consisting of its repetition factors.
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 1972 [alternative scanned copy].
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EXAMPLE
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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.
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CROSSREFS
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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: A082074 A132283 A088370 this_sequence A115624 A076291 A124458
Adjacent sequences: A113784 A113785 A113786 this_sequence A113788 A113789 A113790
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KEYWORD
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easy,nonn
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AUTHOR
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Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jan 20 2006 The new sequences.
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