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A144078 a(n) = the number of digits in the binary representation of n that differ from the corresponding digit in the binary reversal of n. (I.e., a(n) = number of 1's in n XOR A030101(n).) 4
0, 2, 0, 2, 0, 2, 0, 2, 0, 4, 2, 4, 2, 2, 0, 2, 0, 4, 2, 2, 0, 4, 2, 4, 2, 2, 0, 4, 2, 2, 0, 2, 0, 4, 2, 4, 2, 6, 4, 4, 2, 6, 4, 2, 0, 4, 2, 4, 2, 2, 0, 6, 4, 4, 2, 6, 4, 4, 2, 4, 2, 2, 0, 2, 0, 4, 2, 4, 2, 6, 4, 2, 0, 4, 2, 4, 2, 6, 4, 4, 2, 6, 4, 2, 0, 4, 2, 4, 2, 6, 4, 2, 0, 4, 2, 4, 2, 2, 0, 6, 4, 4, 2, 4, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) + A144079(n) = A070939(n), the number of binary digits in n.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

FORMULA

From Rémy Sigrist, Oct 07 2018: (Start)

a(n) = 0 iff n is a binary palindrome (A006995).

a(A143960(n)) = 2*n (in fact A143960(n) is the least k such that a(k) = 2*n).

(End)

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 two bit pairs that differ, so a(20) = 2.

MAPLE

A144078 := 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, ", A144078(n)) ; od: # R. J. Mathar, Sep 14 2008

MATHEMATICA

brd[n_]:=Module[{idn2=IntegerDigits[n, 2]}, Count[Transpose[{idn2, Reverse[ idn2]}], _?(#[[1]]!=#[[2]]&)]]; Array[brd, 110] (* Harvey P. Dale, May 09 2016 *)

PROG

(PARI) a(n) = hammingweight(bitxor(n, fromdigits(Vecrev(binary(n)), 2))) \\ Rémy Sigrist, Oct 07 2018

CROSSREFS

Cf. A006995, A030101, A143960, A144079.

Sequence in context: A096158 A264782 A053471 * A277158 A318282 A281009

Adjacent sequences:  A144075 A144076 A144077 * A144079 A144080 A144081

KEYWORD

base,nonn

AUTHOR

Leroy Quet, Sep 09 2008

EXTENSIONS

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

STATUS

approved

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Last modified May 25 02:01 EDT 2020. Contains 334581 sequences. (Running on oeis4.)