%I A066740
%S A066740 1,1,2,5,13,44,151,614,2446,11066,53368,253927,1316375,7213979
%N A066740 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.
%e A066740 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).
%t A066740 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 ] ]
%Y A066740 Cf. A007504, A066723.
%Y A066740 Sequence in context: A149874 A114297 A119533 this_sequence A000719 A149875 
               A085632
%Y A066740 Adjacent sequences: A066737 A066738 A066739 this_sequence A066741 A066742 
               A066743
%K A066740 more,nonn
%O A066740 0,3
%A A066740 Naohiro Nomoto (n_nomoto(AT)yabumi.com), Jan 16 2002
%E A066740 Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Jan 18 2002