A224702 Number of partition sums between powers of 2 where the partition sums b(k) are A000070 and 2^n <= b(k) < 2^(n+1).

1, 1, 2, 1, 2, 1, 2, 2, 3, 2, 2, 3, 3, 3, 3, 3, 4, 4, 3, 4, 4, 5, 4, 5, 4, 5, 5, 5, 6, 5, 6, 5, 6, 6, 7, 6, 7, 6, 7, 7, 7, 7, 8, 7, 8, 8, 8, 8, 9, 8, 9, 9, 8, 10, 9, 9, 10, 9, 10, 10, 10, 11, 10, 11, 10, 11, 11, 11, 12, 11, 12, 11, 12, 12, 13, 12, 12, 13, 13, 13, 13, 13, 14, 13, 14

Offset: 0

Author

Frank M Jackson, Apr 16 2013

Keywords

• nonn

Comments

The sequence of partition sums A000070 is a complete sequence.

Examples

			a(11) = 3 as between 2048 and 4096 there are 3 partition sums namely 2087, 2714, 3506.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A000070, A036378, A052005

Programs

Mathematica

getterm[n0_] := Sum[PartitionsP[m0], {m0, 0, n0}]; termcount[n1_] := (m1=0; While[getterm[m1]<2^n1, m1++]; m1); Table[termcount[n+1]-termcount[n], {n, 0, 100}]