A143905 Positive integers n that are palindromic in base 2 and whose binary representation has the same number of 0's as 1's.

9, 153, 165, 195, 2289, 2409, 2457, 2661, 2709, 2829, 3171, 3219, 3339, 3591, 34785, 35793, 36273, 36465, 37833, 38313, 38505, 39321, 39513, 39993, 41925, 42405, 42597, 43413, 43605, 44085, 45453, 45645, 46125, 47133, 50115, 50595, 50787

Offset

1,1

Comments

Every term of this sequence corresponds to a different term of sequence A031443 (Numbers that in base 2 have the same number of 0's as 1's). (See formula.) - Leroy Quet, Sep 05 2008

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Formula

a(n) = A031443(n)*2^A070939(A031443(n)) + A030101(A031443(n)). - Leroy Quet, Sep 05 2008

Intersection of A031443 and A006995. - R. J. Mathar, Sep 05 2008

Example

165 in binary is 10100101. This binary representation is a palindrome. And it has both four 0's and four 1's. So 165 is in the sequence.

Mathematica

Select[Range[100000], Reverse[IntegerDigits[ #, 2]] == IntegerDigits[ #, 2] && DigitCount[ #, 2, 0] == DigitCount[ #, 2, 1] &] (* Stefan Steinerberger, Sep 05 2008 *)

Prog

(PARI) isok(n) = {my(b = binary(n)); (Vecrev(b) == b) && (hammingweight(n) == #b/2); } \\ Michel Marcus, Aug 01 2017

Crossrefs

Cf. A006995, A031443, A143906.

Sequence in context: A326012 A089916 A143000 * A274502 A249642 A093849

Adjacent sequences: A143902 A143903 A143904 * A143906 A143907 A143908

Keyword

base,nonn

Author

Leroy Quet, Sep 04 2008

Extensions

More terms from Stefan Steinerberger and R. J. Mathar, Sep 05 2008

Status

approved