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Search: id:A066740
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| A066740 |
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Number of distinct partitions of A007504(n) which can be obtained by merging parts in the partition 2+3+5+...+prime(n), where prime(n) is the n-th prime. |
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+0
2
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| 1, 1, 2, 5, 13, 44, 151, 614, 2446, 11066, 53368, 253927, 1316375, 7213979
(list; graph; listen)
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OFFSET
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0,3
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EXAMPLE
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For n=4, the 13 partitions are 17, 2+15, 3+14, 5+12, 7+10, 8+9, 2+3+12, 2+5+10, 2+7+8, 3+5+9, 3+7+7, 5+5+7, 2+3+5+7. 5+12 and 7+10 can be obtained in two ways each: 5+12 = (5)+(2+3+7) = (2+3)+(5+7), 7+10 = (7)+(2+3+5) = (2+5)+(3+7).
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MATHEMATICA
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addto[ p_, k_ ] := Module[ {}, lth=Length[ p ]; Union[ Sort/@Append[ Table[ Join[ Take[ p, i-1 ], {p[ [ i ] ]+k}, Take[ p, i-lth ] ], {i, 1, lth} ], Append[ p, k ] ] ] ]; addtolist[ plist_, k_ ] := Union[ Join@@(addto[ #, k ]&/@plist) ]; l[ 0 ]={{}}; l[ n_ ] := l[ n ]=addtolist[ l[ n-1 ], Prime[ n ] ]; a[ n_ ] := Length[ l[ n ] ]
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CROSSREFS
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Cf. A007504, A066723.
Sequence in context: A149874 A114297 A119533 this_sequence A000719 A149875 A085632
Adjacent sequences: A066737 A066738 A066739 this_sequence A066741 A066742 A066743
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KEYWORD
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more,nonn
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AUTHOR
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Naohiro Nomoto (n_nomoto(AT)yabumi.com), Jan 16 2002
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EXTENSIONS
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Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Jan 18 2002
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