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