cp's OEIS Frontend

A331855 a(n) is the number of distinct values obtained by partitioning the binary representation of n into consecutive blocks, and then reversing those blocks.

%I A331855 #13 Feb 02 2020 14:35:44
%S A331855 1,1,2,1,3,3,3,1,4,6,5,4,5,4,4,1,5,10,9,9,8,8,9,5,7,9,8,5,7,5,5,1,6,
%T A331855 15,14,16,12,16,18,12,11,16,13,12,15,13,14,6,9,16,15,13,13,12,12,6,10,
%U A331855 12,11,6,9,6,6,1,7,21,20,25,18,27,30,22,16,27,25
%N A331855 a(n) is the number of distinct values obtained by partitioning the binary representation of n into consecutive blocks, and then reversing those blocks.
%H A331855 Rémy Sigrist, <a href="/A331855/b331855.txt">Table of n, a(n) for n = 0..16384</a>
%H A331855 Rémy Sigrist, <a href="/A331855/a331855.gp.txt">PARI program for A331855</a>
%H A331855 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A331855 a(2^k-1) = 1 for any k >= 0.
%F A331855 a(2^k) = k+1 for any k >= 0.
%F A331855 a(2^k+1) = A000217(k) for any k > 0.
%F A331855 a(2^k+2) = A000096(k-1) for any k > 3.
%F A331855 a(2^k+3) = (k-1)^2 for any k > 1.
%e A331855 For n = 6:
%e A331855 - the binary representation of 6 is "110",
%e A331855 - we can split it in 4 ways:
%e A331855       "110" -> "011" -> 3
%e A331855       "1" and "10" -> "1" and "01" -> 5
%e A331855       "11" and "0" -> "11" and "0" -> 6
%e A331855       "1" and "1" and "0" -> "1" and "1" and "0" -> 6
%e A331855 - we have 3 distinct values,
%e A331855 - hence a(6) = 3.
%o A331855 (PARI) See Links section.
%Y A331855 See A331851 for similar sequences.
%Y A331855 See A331856 and A331857 for the least and greatest values, respectively.
%Y A331855 Cf. A000096, A000217.
%K A331855 nonn,base
%O A331855 0,3
%A A331855 _Rémy Sigrist_, Jan 29 2020