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 A206913 Greatest binary palindrome <= n; the binary palindrome floor function. 77
 0, 1, 1, 3, 3, 5, 5, 7, 7, 9, 9, 9, 9, 9, 9, 15, 15, 17, 17, 17, 17, 21, 21, 21, 21, 21, 21, 27, 27, 27, 27, 31, 31, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 45, 45, 45, 45, 45, 45, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 63, 63, 65, 65, 65, 65 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Also the greatest binary palindrome < n + 1; For n > 0, a(n-1) is the greatest binary palindrome < n. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 FORMULA Let n > 2, p = 1 + 2*floor((n-1)/2), m = floor(log_2(p)), q = floor((m+1)/2), s = floor(log_2(p-2^q)), F(x, r) = floor(x/2^q)*2^q + Sum_{k = 0...q - 1} (floor(x/2^(r-k)) mod 2)*2^k; If F(p, m) <= n then a(n) = F(p, m), otherwise a(n) = F(p-2^q, s). By definition: F(p, m) = floor(p/2^q)*2^q + A030101(p) mod 2^q; also: F(p-2^q, s) = floor((p-2^q)/2^q)*2^q + A030101(p-2^q) mod 2^q; [Edited and corrected by Hieronymus Fischer, Sep 08 2018] a(n) = A006995(A206915(n)); a(n) = A006995(A206915(A206914(n+1))-1); a(n) = A006995(A206916(A206914(n+1))-1). EXAMPLE a(0) = 0 since 0 is the greatest binary palindrome <= 0; a(1) = 1 since 1 is the greatest binary palindrome <= 1; a(2) = 1 since 1 is the greatest binary palindrome <= 2; a(3) = 3 since 3 is the greatest binary palindrome <= 3. PROG (Haskell) a206913 n = last \$ takeWhile (<= n) a006995_list -- Reinhard Zumkeller, Feb 27 2012 CROSSREFS Cf. A006995, A206915, A206920, A030301. Sequences related to palindromic floor and ceiling: A175298, A206913, A206914, A261423, A262038, and the large block of consecutive sequences beginning at A265509. Sequence in context: A129337 A133909 A177691 * A117767 A293701 A296063 Adjacent sequences:  A206910 A206911 A206912 * A206914 A206915 A206916 KEYWORD nonn,base AUTHOR Hieronymus Fischer, Feb 13 2012 STATUS approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)