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A331856 a(n) is the least value obtained by partitioning the binary representation of n into consecutive blocks, and then reversing those blocks.

%I A331856 #11 Feb 01 2020 18:22:59
%S A331856 0,1,1,3,1,3,3,7,1,3,5,7,3,7,7,15,1,3,5,7,5,11,11,15,3,7,11,15,7,15,
%T A331856 15,31,1,3,5,7,9,11,11,15,5,11,21,23,13,23,23,31,3,7,13,15,11,23,27,
%U A331856 31,7,15,23,31,15,31,31,63,1,3,5,7,9,11,11,15,9,19,21
%N A331856 a(n) is the least value obtained by partitioning the binary representation of n into consecutive blocks, and then reversing those blocks.
%H A331856 Rémy Sigrist, <a href="/A331856/b331856.txt">Table of n, a(n) for n = 0..16384</a>
%H A331856 Rémy Sigrist, <a href="/A331856/a331856.gp.txt">PARI program for A331856</a>
%H A331856 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A331856 a(n)^A023416(n) = A038573(n) (where a^k denotes the k-th iterate of a).
%F A331856 a(n) <= n with equality iff n belongs to A000225.
%e A331856 For n = 6:
%e A331856 - the binary representation of 6 is "110",
%e A331856 - we can split it in 4 ways:
%e A331856       "110" -> "011" -> 3
%e A331856       "1" and "10" -> "1" and "01" -> 5
%e A331856       "11" and "0" -> "11" and "0" -> 6
%e A331856       "1" and "1" and "0" -> "1" and "1" and "0" -> 6
%e A331856 - we have 3 distinct values, the least being 3,
%e A331856 - hence a(6) = 3.
%o A331856 (PARI) See Links section.
%Y A331856 See A331855 for the number of distinct values, and A331857 for the greatest value.
%Y A331856 Cf. A000225, A023416, A038573.
%K A331856 nonn,base
%O A331856 0,4
%A A331856 _Rémy Sigrist_, Jan 29 2020