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A330717 a(n) is the greatest binary palindrome of the form floor(n/2^k) with k >= 0.

%I A330717 #12 Jan 01 2020 11:24:32
%S A330717 0,1,1,3,1,5,3,7,1,9,5,5,3,3,7,15,1,17,9,9,5,21,5,5,3,3,3,27,7,7,15,
%T A330717 31,1,33,17,17,9,9,9,9,5,5,21,21,5,45,5,5,3,3,3,51,3,3,27,27,7,7,7,7,
%U A330717 15,15,31,63,1,65,33,33,17,17,17,17,9,73,9,9,9,9
%N A330717 a(n) is the greatest binary palindrome of the form floor(n/2^k) with k >= 0.
%C A330717 In other words, a(n) is the greatest binary palindromic prefix of n.
%H A330717 Rémy Sigrist, <a href="/A330717/b330717.txt">Table of n, a(n) for n = 0..8192</a>
%H A330717 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A330717 A070939(a(n)) = A215467(n).
%F A330717 a(n) = 1 iff n is a power of 2.
%F A330717 a(n) <= n with equality iff n is a binary palindrome (A006995).
%F A330717 a(a(n)) = a(n).
%F A330717 a(2*n) = a(n).
%e A330717 The first terms, alongside the binary representations of n and of a(n), are:
%e A330717   n   a(n)  bin(n)  bin(a(n))
%e A330717   --  ----  ------  ---------
%e A330717    0     0       0          0
%e A330717    1     1       1          1
%e A330717    2     1      10          1
%e A330717    3     3      11         11
%e A330717    4     1     100          1
%e A330717    5     5     101        101
%e A330717    6     3     110         11
%e A330717    7     7     111        111
%e A330717    8     1    1000          1
%e A330717    9     9    1001       1001
%e A330717   10     5    1010        101
%e A330717   11     5    1011        101
%o A330717 (PARI) a(n,b=2) = { my (d=digits(n,b)); forstep (w=#d, 1, -1, my (h=d[1..w]); if (h==Vecrev(h), return (fromdigits(h, b)))); return (0) }
%Y A330717 Cf. A006995, A215467.
%K A330717 nonn,base,easy
%O A330717 0,4
%A A330717 _Rémy Sigrist_, Dec 28 2019