A055945 a(n) = n - (reversal of base-2 digits of n) (and then the result is written in base 10).

0, 0, 1, 0, 3, 0, 3, 0, 7, 0, 5, -2, 9, 2, 7, 0, 15, 0, 9, -6, 15, 0, 9, -6, 21, 6, 15, 0, 21, 6, 15, 0, 31, 0, 17, -14, 27, -4, 13, -18, 35, 4, 21, -10, 31, 0, 17, -14, 45, 14, 31, 0, 41, 10, 27, -4, 49, 18, 35, 4, 45, 14, 31, 0, 63, 0, 33, -30, 51, -12, 21, -42, 63, 0, 33, -30, 51, -12, 21, -42, 75, 12, 45, -18, 63, 0, 33, -30, 75, 12, 45

Offset: 0

Author

Henry Bottomley, Jul 18 2000

Keywords

• base
• sign
• look

Comments

a(n) is even if n is odd and a(n) is odd if n is even; this is caused by the kind of swapping the most significant and least significant binary digit when reversing n and the fact that the most significant digit of n is always 1. - R. J. Mathar, Nov 05 2015

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..16384
• Rémy Sigrist, Colored scatterplot of the first 2^16 terms (where the color is function of n mod 8)

Crossrefs

Cf. A030101, A030109, A265326.

Programs

Maple

a:= proc(n) local m, r; m:=n; r:=0;
      while m>0 do r:= r*2 +irem(m, 2, 'm') od;
      n-r
    end:
seq(a(n), n=0..100);  # Alois P. Heinz, Jul 02 2015

Mathematica

Array[# - IntegerReverse[#, 2] &, 90, 0] (* Michael De Vlieger, Sep 06 2019 *)

Formula

For 2^m <= n <= 2^(m+1), we have n - 2^(m+1) <= a(n) <= n. - N. J. A. Sloane, May 29 2016

a(n) = n - A030101(n).