A331851 - OEIS

%I #10 Jan 31 2020 20:27:47

%S 1,1,2,2,2,4,3,3,2,5,4,7,3,7,4,5,2,6,5,9,4,7,7,11,3,9,7,11,4,11,6,7,2,

%T 7,6,11,5,11,9,14,4,11,7,15,7,15,11,17,3,11,9,13,7,15,11,19,4,14,11,

%U 19,6,17,8,11,2,8,7,13,6,13,11,17,5,10,11,21,9

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

%C This sequence is a variant of A321318.

%H Rémy Sigrist, <a href="/A331851/a331851.gp.txt">PARI program for A331851</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) = k+2 for any k > 1.

%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*2 = 2

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

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

%e - we have 3 distinct values,

%e - hence a(6) = 3.

%o (PARI) See Links section.

%Y Cf. A321318 (additive variant).

%Y Cf. A331852 (XOR variant), A331853 (AND variant), A331854 (OR variant).

%Y Cf. A331855 (reverse variant).

%K nonn,base

%O 0,3

%A _Rémy Sigrist_, Jan 29 2020