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A057891 In base 2, neither a palindrome nor becomes a palindrome if trailing 0's are omitted. 8
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
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.
Sequence in context: A005360 A269806 A062019 * A164708 A030792 A101934
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 May 22 21:38 EDT 2024. Contains 372758 sequences. (Running on oeis4.)