A057891 In base 2, neither a palindrome nor becomes a palindrome if trailing 0's are omitted.

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

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