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A143905
Positive integers n that are palindromic in base 2 and whose binary representation has the same number of 0's as 1's.
2
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
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
KEYWORD
base,nonn
AUTHOR
Leroy Quet, Sep 04 2008
EXTENSIONS
More terms from Stefan Steinerberger and R. J. Mathar, Sep 05 2008
STATUS
approved