

A145799


a(n) = the largest integer that is an (odd) palindrome when represented in binary and that occurs in the binary representation of n.


4



1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 5, 3, 5, 7, 15, 1, 17, 9, 9, 5, 21, 5, 7, 3, 9, 5, 27, 7, 7, 15, 31, 1, 33, 17, 17, 9, 9, 9, 9, 5, 9, 21, 21, 5, 45, 7, 15, 3, 17, 9, 51, 5, 21, 27, 27, 7, 9, 7, 27, 15, 15, 31, 63, 1, 65, 33, 33, 17, 17, 17, 17, 9, 73, 9, 9, 9, 9, 9, 15, 5, 17, 9, 9, 21, 85, 21, 21
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OFFSET

1,3


COMMENTS

The binary expansion of a(n) is the largest (odd) palindrome that appears as a substring of the binary expansion of n. Nonzero binary palindromes are necessarily odd (see A006995).
For n = 2^k, a(n) = 1 is the largest binary palindrome in the binary representation of n.
a(2^k*A006995(n)) = A006995(n).  Ray Chandler, Oct 26 2008
a(m) = m iff m is a palindrome: a(A006995(n)) = A006995(n), a(A154809(n)) < A154809(n).  Reinhard Zumkeller, Sep 24 2015


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..16384


EXAMPLE

20 in binary is 10100. The largest binary palindrome included in this binary representation is 101, which is 5 in decimal. So a(20) = 5.


MATHEMATICA

Block[{nn = 87, s}, s = Reverse@ Select[IntegerDigits[#, 2] & /@ Range[2^Log2@ nn], PalindromeQ]; Table[With[{d = IntegerDigits[n, 2]}, FromDigits[#, 2] &@ SelectFirst[s, SequenceCount[d, #] > 0 &]], {n, nn}]] (* Michael De Vlieger, Sep 23 2017 *)


PROG

(Haskell)
a145799 = maximum . map (foldr (\b v > 2 * v + b) 0) .
filter (\bs > bs == reverse bs && head bs == 1) .
substr . bin where
substr [] = []
substr us'@(_:us) = sub us' ++ substr us where
sub [] = []; sub (v:vs) = [v] : [v : ws  ws < sub vs ]
bin 0 = []; bin n = b : bin n' where (n', b) = divMod n 2
 Reinhard Zumkeller, Sep 24 2015


CROSSREFS

Cf. A006995, A145800.
Cf. A154809.
Sequence in context: A211206 A330717 A036233 * A331804 A244568 A331471
Adjacent sequences: A145796 A145797 A145798 * A145800 A145801 A145802


KEYWORD

base,nonn,look


AUTHOR

Leroy Quet, Oct 19 2008


EXTENSIONS

Extended by Ray Chandler, Oct 26 2008


STATUS

approved



