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A253581 a(n) = A252867(n) AND A252867(n+2).

%I A253581 #6 Jan 13 2015 07:33:31
%S A253581 0,1,2,4,2,4,1,4,1,2,8,2,8,1,8,32,10,32,3,32,16,8,16,13,16,2,16,34,20,
%T A253581 1,20,1,2,1,2,4,8,4,8,6,64,18,64,18,65,48,65,36,65,44,1,14,1,2,1,2,4,
%U A253581 2,4,3,32,2,48,66,33,66,37,16,37,16,5,24,128,26
%N A253581 a(n) = A252867(n) AND A252867(n+2).
%C A253581 Binary coded intersection of the two sets, coded by A252867(n) and A252867(n+2);
%C A253581 for n > 0: a(n) > 0 by definition of A252867;
%C A253581 conjecture: all natural numbers occur, cf. A253603, giving smallest m such that A253581(m) = n.
%H A253581 Reinhard Zumkeller, <a href="/A253581/b253581.txt">Table of n, a(n) for n = 0..10000</a>
%e A253581 .   n | A252867(n) |   binary |   a(n) |  binary
%e A253581 . ----+------------+----------+--------+---------
%e A253581 .   0 |          0 |        0 |      0 |       0
%e A253581 .   1 |          1 |        1 |      1 |       1
%e A253581 .   2 |          2 |       10 |      2 |      10
%e A253581 .   3 |          5 |      101 |      4 |     100
%e A253581 .   4 |         10 |     1010 |      2 |      10
%e A253581 .   5 |          4 |      100 |      4 |     100
%e A253581 .   6 |          3 |       11 |      1 |       1
%e A253581 .   7 |         12 |     1100 |      4 |     100
%e A253581 .   8 |         17 |    10001 |      1 |       1
%e A253581 .   9 |          6 |      110 |      2 |      10
%e A253581 .  10 |          9 |     1001 |      8 |    1000
%e A253581 .  11 |         18 |    10010 |      2 |      10
%e A253581 .  12 |          8 |     1000 |      8 |    1000
%e A253581 .  13 |          7 |      111 |      1 |       1
%e A253581 .  14 |         24 |    11000 |      8 |    1000
%e A253581 .  15 |         33 |   100001 |     32 |  100000
%e A253581 .  16 |         14 |     1110 |     10 |    1010
%e A253581 .  17 |         32 |   100000 |     32 |  100000
%e A253581 .  18 |         11 |     1011 |      3 |      11
%e A253581 .  19 |         36 |   100100 |     32 |  100000
%e A253581 .  20 |         19 |    10011 |     16 |   10000
%e A253581 .  21 |         40 |   101000 |      8 |    1000
%e A253581 .  22 |         16 |    10000 |     16 |   10000
%e A253581 .  23 |         13 |     1101 |     13 |    1101
%e A253581 .  24 |         48 |   110000 |     16 |   10000
%e A253581 .  25 |         15 |     1111 |      2 |      10
%e A253581 .  26 |         80 |  1010000 |     16 |   10000
%e A253581 .  27 |         34 |   100010 |     34 |  100010
%e A253581 .  28 |         20 |    10100 |     20 |   10100
%e A253581 .  29 |         35 |   100011 |      1 |       1
%e A253581 .  30 |         28 |    11100 |     20 |   10100 .
%o A253581 (Haskell)
%o A253581 import Data.Bits ((.&.))
%o A253581 a253581 n = a253581_list !! n
%o A253581 a253581_list = zipWith (.&.) a252867_list $ drop 2 a252867_list :: [Int]
%Y A253581 Cf. A252867, A253603, A253582, A251102, A007088.
%K A253581 nonn
%O A253581 0,3
%A A253581 _Reinhard Zumkeller_, Jan 12 2015