A144079 a(n) = the number of digits in the binary representation of n that equal the corresponding digit in the binary reversal of n. (I.e., a(n) = number of 0's in n XOR A030101(n).)

1, 0, 2, 1, 3, 1, 3, 2, 4, 0, 2, 0, 2, 2, 4, 3, 5, 1, 3, 3, 5, 1, 3, 1, 3, 3, 5, 1, 3, 3, 5, 4, 6, 2, 4, 2, 4, 0, 2, 2, 4, 0, 2, 4, 6, 2, 4, 2, 4, 4, 6, 0, 2, 2, 4, 0, 2, 2, 4, 2, 4, 4, 6, 5, 7, 3, 5, 3, 5, 1, 3, 5, 7, 3, 5, 3, 5, 1, 3, 3, 5, 1, 3, 5, 7, 3, 5, 3, 5, 1, 3, 5, 7, 3, 5, 3, 5, 5, 7, 1, 3, 3, 5, 3, 5

Offset

1,3

Comments

A144078(n) + a(n) = A070939(n), the number of binary digits in n.

Links

Table of n, a(n) for n=1..105.

Example

20 in binary is 10100. Compare this with its digit reversal, 00101. XOR each pair of corresponding digits: 1 XOR 0 = 1, 0 XOR 0 = 0, 1 XOR 1 = 0, 0 XOR 0 = 0, 0 XOR 1 = 1. There are three bit pairs that contain the same values, so a(20) = 3.

Maple

A144079 := proc(n) local a, dgs, i; a := 0 ; dgs := convert(n, base, 2) ; for i from 1 to nops(dgs) do if op(i, dgs)+op(-i, dgs) <> 1 then a := a+1 ; fi; od; RETURN(a) ; end: for n from 1 to 240 do printf("%d, ", A144079(n)) ; od: # R. J. Mathar, Sep 14 2008

Mathematica

Table[With[{c=IntegerDigits[n, 2]}, Count[BitXor[c, Reverse[c]], 0]], {n, 110}] (* Harvey P. Dale, Sep 03 2015 *)

Crossrefs

Cf. A030101, A144078.

Sequence in context: A109698 A029231 A025808 * A326839 A071575 A307908

Adjacent sequences: A144076 A144077 A144078 * A144080 A144081 A144082

Keyword

base,nonn

Author

Leroy Quet, Sep 09 2008

Extensions

More terms from R. J. Mathar, Sep 14 2008

Status

approved