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.

1, 1, 2, 5, 13, 44, 151, 614, 2446, 11066, 53368, 253927, 1316375, 7213979, 38175696, 213766427

Offset: 0

Author

Naohiro Nomoto, Jan 16 2002

Keywords

• more
• nonn

Examples

			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).
		

Crossrefs

Cf. A007504, A066723.

Programs

Maple

b:= proc(n) local p; p:= `if`(n=0, 1, ithprime(n));
      b(n):= `if`(n<2, {[p$n]}, map(x-> [sort([x[], p]),
      seq(sort(subsop(i=x[i]+p, x)), i=1..nops(x))][], b(n-1)))
    end:
a:= n-> nops(b(n)):
seq(a(n), n=0..10);  # Alois P. Heinz, May 31 2013

Mathematica

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 ] ]

Extensions

Edited by Dean Hickerson, Jan 18 2002

a(14)-a(15) from Sean A. Irvine, Nov 05 2023