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

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, 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, 2, 4, 3, 32, 2, 48, 66, 33, 66, 37, 16, 37, 16, 5, 24, 128, 26

Offset: 0

Author

Reinhard Zumkeller, Jan 12 2015

Keywords

• nonn

Comments

Binary coded intersection of the two sets, coded by A252867(n) and A252867(n+2);

for n > 0: a(n) > 0 by definition of A252867;

conjecture: all natural numbers occur, cf. A253603, giving smallest m such that A253581(m) = n.

Examples

			.   n | A252867(n) |   binary |   a(n) |  binary
. ----+------------+----------+--------+---------
.   0 |          0 |        0 |      0 |       0
.   1 |          1 |        1 |      1 |       1
.   2 |          2 |       10 |      2 |      10
.   3 |          5 |      101 |      4 |     100
.   4 |         10 |     1010 |      2 |      10
.   5 |          4 |      100 |      4 |     100
.   6 |          3 |       11 |      1 |       1
.   7 |         12 |     1100 |      4 |     100
.   8 |         17 |    10001 |      1 |       1
.   9 |          6 |      110 |      2 |      10
.  10 |          9 |     1001 |      8 |    1000
.  11 |         18 |    10010 |      2 |      10
.  12 |          8 |     1000 |      8 |    1000
.  13 |          7 |      111 |      1 |       1
.  14 |         24 |    11000 |      8 |    1000
.  15 |         33 |   100001 |     32 |  100000
.  16 |         14 |     1110 |     10 |    1010
.  17 |         32 |   100000 |     32 |  100000
.  18 |         11 |     1011 |      3 |      11
.  19 |         36 |   100100 |     32 |  100000
.  20 |         19 |    10011 |     16 |   10000
.  21 |         40 |   101000 |      8 |    1000
.  22 |         16 |    10000 |     16 |   10000
.  23 |         13 |     1101 |     13 |    1101
.  24 |         48 |   110000 |     16 |   10000
.  25 |         15 |     1111 |      2 |      10
.  26 |         80 |  1010000 |     16 |   10000
.  27 |         34 |   100010 |     34 |  100010
.  28 |         20 |    10100 |     20 |   10100
.  29 |         35 |   100011 |      1 |       1
.  30 |         28 |    11100 |     20 |   10100 .
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A252867, A253603, A253582, A251102, A007088.

Programs

Haskell

import Data.Bits ((.&.))
a253581 n = a253581_list !! n
a253581_list = zipWith (.&.) a252867_list $ drop 2 a252867_list :: [Int]