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 A057891 In base 2, neither a palindrome nor becomes a palindrome if trailing 0's are omitted. 7
 11, 13, 19, 22, 23, 25, 26, 29, 35, 37, 38, 39, 41, 43, 44, 46, 47, 49, 50, 52, 53, 55, 57, 58, 59, 61, 67, 69, 70, 71, 74, 75, 76, 77, 78, 79, 81, 82, 83, 86, 87, 88, 89, 91, 92, 94, 95, 97, 98, 100, 101, 103, 104, 105, 106, 109, 110, 111, 113, 114, 115, 116, 117, 118 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS These could be called "asymmetric bit strings". Fixed pairs of A057889, complement of A057890. If these numbers are converted to their binary polynomial, one of the roots of that polynomial will have absolute values other than 1 or 0. For example 11 = 2^3 + 2^1 + 2^0, the absolute values of the roots of x^3 + x + 1 are 0.682328... and 1.21061... which are not 1 or 0, so 11 is in the sequence. The first number with this property which is not a term is A057890(53) = 107. - Benedict W. J. Irwin, Sep 07 2017 and Andrey Zabolotskiy, Oct 13 2017 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA A030101(A030101(n)) != A030101(n). - David Wilson, Jun 09 2009, Jun 18 2009 A178225(A000265(a(n))) = 0. - Reinhard Zumkeller, Oct 21 2011 EXAMPLE 11 is included because 1011 is asymmetrical, but 12 is not because 001100 is a palindrome. PROG (Haskell) a057891 n = a057891_list !! (n-1) a057891_list = filter ((== 0) . a178225 . a000265) [1..] -- Reinhard Zumkeller, Oct 21 2011 CROSSREFS Cf. A061917, A006995. Complement of A057890. Cf. A030101, A000265, A006519, A057889. Sequence in context: A005360 A269806 A062019 * A164708 A030792 A101934 Adjacent sequences: A057888 A057889 A057890 * A057892 A057893 A057894 KEYWORD easy,nonn,base AUTHOR Marc LeBrun, Sep 25 2000 EXTENSIONS Edited by N. J. A. Sloane, Jun 09 2009 at the suggestion of Ray Chandler A-numbers in formula corrected by R. J. Mathar, Jun 18 2009 STATUS approved

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Last modified December 9 23:05 EST 2022. Contains 358710 sequences. (Running on oeis4.)