cp's OEIS Frontend

A331851 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.

%I A331851 #10 Jan 31 2020 20:27:47
%S A331851 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 A331851 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 A331851 19,6,17,8,11,2,8,7,13,6,13,11,17,5,10,11,21,9
%N A331851 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 A331851 This sequence is a variant of A321318.
%H A331851 Rémy Sigrist, <a href="/A331851/a331851.gp.txt">PARI program for A331851</a>
%H A331851 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A331851 a(2^k) = 2 for any k > 0.
%F A331851 a(2^k+1) = k+2 for any k > 1.
%e A331851 For n = 6:
%e A331851 - the binary representation of 6 is "110",
%e A331851 - we can split it in 4 ways:
%e A331851       "110" -> 6
%e A331851       "1" and "10" -> 1*2 = 2
%e A331851       "11" and "0" -> 3*0 = 0
%e A331851       "1" and "1" and "0" -> 1*1*0 = 0
%e A331851 - we have 3 distinct values,
%e A331851 - hence a(6) = 3.
%o A331851 (PARI) See Links section.
%Y A331851 Cf. A321318 (additive variant).
%Y A331851 Cf. A331852 (XOR variant), A331853 (AND variant), A331854 (OR variant).
%Y A331851 Cf. A331855 (reverse variant).
%K A331851 nonn,base
%O A331851 0,3
%A A331851 _Rémy Sigrist_, Jan 29 2020