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