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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...)).

%I A059902 #7 Oct 18 2022 13:42:51
%S A059902 0,1,4,3,5,6,11,16,7,36,14,139,17,18,37,15,44,142,32907,20,19,48,39,
%T A059902 26,45,2084,143,172,32910,2147516555,21,22,49,50,27,56,47,2085,154,
%U A059902 173,2212,32911,32940,2147516558,9223372039002292363,64,23,52,51,528,30,57
%N 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...)).
%C A059902 Partitions are ordered canonically (as described in the OEIS Wiki link): [] [1] [2] [1+1] [3] [2+1] [1+1+1] [4]...
%H A059902 OEIS Wiki, <a href="/wiki/Partitions#Orderings_of_partitions">Orderings of partitions</a>
%F A059902 a(n) = A059884(A059901(n)).
%e A059902 Partition for n=17 is [2+2+1], so a(17) is given by
%e A059902 .....0 0 0 0 0 1 0- -> 2
%e A059902 ..... . 0 . 1 . 0 - -> 2
%e A059902 ..... 0 ..... 1 ... -> 1
%e A059902 ------------------
%e A059902 .....0000000101100 = 44.
%Y A059902 Cf. A059901, A059884, A000041.
%K A059902 base,easy,nonn
%O A059902 0,3
%A A059902 _Marc LeBrun_, Feb 07 2001
%E A059902 Terms reordered by _Sean A. Irvine_, Oct 17 2022