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A331857 a(n) is the greatest value obtained by partitioning the binary representation of n into consecutive blocks, and then reversing those blocks.

%I A331857 #10 Feb 03 2020 02:10:38
%S A331857 0,1,2,3,4,6,6,7,8,12,12,14,12,14,14,15,16,24,24,28,24,26,28,30,24,28,
%T A331857 28,30,28,30,30,31,32,48,48,56,48,52,56,60,48,52,52,58,56,58,60,62,48,
%U A331857 56,56,60,56,58,60,62,56,60,60,62,60,62,62,63,64,96,96
%N A331857 a(n) is the greatest value obtained by partitioning the binary representation of n into consecutive blocks, and then reversing those blocks.
%H A331857 Rémy Sigrist, <a href="/A331857/b331857.txt">Table of n, a(n) for n = 0..16384</a>
%H A331857 Rémy Sigrist, <a href="/A331857/a331857.gp.txt">PARI program for A331857</a>
%H A331857 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A331857 a(n)^A023416(n) = A073138(n) (where a^k denotes the k-th iterate of n).
%F A331857 a(n) >= n with equality iff n belongs to A023758.
%e A331857 For n = 6:
%e A331857 - the binary representation of 6 is "110",
%e A331857 - we can split it in 4 ways:
%e A331857       "110" -> "011" -> 3
%e A331857       "1" and "10" -> "1" and "01" -> 5
%e A331857       "11" and "0" -> "11" and "0" -> 6
%e A331857       "1" and "1" and "0" -> "1" and "1" and "0" -> 6
%e A331857 - we have 3 distinct values, the greatest being 6,
%e A331857 - hence a(6) = 6.
%o A331857 (PARI) See Links section.
%Y A331857 See A331855 for the number of distinct values, and A331856 for the least value.
%Y A331857 Cf. A023416, A023758, A073138.
%K A331857 nonn,base
%O A331857 0,3
%A A331857 _Rémy Sigrist_, Jan 29 2020