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

Author

Leroy Quet, Sep 04 2008

Keywords

• base
• nonn

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A006995, A031443, A143906.

Programs

Mathematica

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

PARI

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

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

Extensions

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