A331853 - OEIS

%I #8 Jan 31 2020 16:05:32

%S 1,1,2,2,2,3,2,2,2,3,3,4,2,3,3,3,2,3,3,4,2,3,3,4,2,3,3,5,2,3,3,3,2,3,

%T 3,4,3,4,4,5,2,3,3,4,3,4,4,6,2,3,3,5,3,4,4,5,2,3,3,5,3,4,4,4,2,3,3,4,

%U 3,4,4,5,2,3,3,4,3,4,4,6,2,3,3,4,3,4,4

%N a(n) is the number of distinct values obtained by partitioning the binary representation of n into consecutive blocks, and then applying the bitwise AND operator to the numbers represented by the blocks.

%H Rémy Sigrist, <a href="/A331853/a331853.gp.txt">PARI program for A331853</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%F a(2^k) = 2 for any k > 0.

%F a(2^k-1) = A008619(k+1) for any k >= 0.

%e For n = 6:

%e - the binary representation of 6 is "110",

%e - we can split it in 4 ways:

%e       "110" -> 6

%e       "1" and "10" -> 1 AND 2 = 0

%e       "11" and "0" -> 3 AND 0 = 0

%e       "1" and "1" and "0" -> 1 AND 1 AND 0 = 0

%e - we have 2 distinct values,

%e - hence a(6) = 2.

%o (PARI) See Links section.

%Y See A331851 for similar sequences.

%Y Cf. A008619.

%K nonn,base

%O 0,3

%A _Rémy Sigrist_, Jan 29 2020