A059902 Partitions encoded by interleaving bits in parts. The partition [P1+P2+P3+...] with P1>=P2>=P3>=... is encoded in binary by recursively interleaving the bits of P1 with the (recursively interleaved bits of P2 with the (recursively...)).

0, 1, 4, 3, 5, 6, 11, 16, 7, 36, 14, 139, 17, 18, 37, 15, 44, 142, 32907, 20, 19, 48, 39, 26, 45, 2084, 143, 172, 32910, 2147516555, 21, 22, 49, 50, 27, 56, 47, 2085, 154, 173, 2212, 32911, 32940, 2147516558, 9223372039002292363, 64, 23, 52, 51, 528, 30, 57

Offset: 0

Author

Marc LeBrun, Feb 07 2001

Keywords

• base
• easy
• nonn

Comments

Partitions are ordered canonically (as described in the OEIS Wiki link): [] [1] [2] [1+1] [3] [2+1] [1+1+1] [4]...

Examples

			Partition for n=17 is [2+2+1], so a(17) is given by
.....0 0 0 0 0 1 0- -> 2
..... . 0 . 1 . 0 - -> 2
..... 0 ..... 1 ... -> 1
------------------
.....0000000101100 = 44.
		

Links

• OEIS Wiki, Orderings of partitions

Crossrefs

Cf. A059901, A059884, A000041.

Formula

a(n) = A059884(A059901(n)).

Extensions

Terms reordered by Sean A. Irvine, Oct 17 2022