A088161 n rotated one binary place to the right less n rotated one binary place to the left.

0, 0, 0, 0, 1, 3, -2, 0, 3, 9, 0, 6, -3, 3, -6, 0, 7, 21, 4, 18, 1, 15, -2, 12, -5, 9, -8, 6, -11, 3, -14, 0, 15, 45, 12, 42, 9, 39, 6, 36, 3, 33, 0, 30, -3, 27, -6, 24, -9, 21, -12, 18, -15, 15, -18, 12, -21, 9, -24, 6, -27, 3, -30, 0, 31, 93, 28, 90, 25, 87, 22, 84, 19, 81, 16, 78, 13, 75, 10, 72, 7, 69, 4

Offset: 0

Author

Robert G. Wilson v, Sep 13 2003

Keywords

• sign
• base
• look

Comments

f(n) is negative about 2/7 of the time to 10^7. f(n) is zero, see A088163.

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A006257, A038572, A088163.

Programs

Maple

f:= proc(n) local a,b;
  if n::even then a:= n/2 else a:= 2^ilog2(n) + (n-1)/2 fi;
  if n = 0 then b:= 0 else b:= 2*n + 1 - 2^(ilog2(n)+1) fi;
  a-b
end proc:
map(f, [$0..200]); # Robert Israel, Mar 03 2025

Mathematica

f[n_] := FromDigits[ RotateRight[ IntegerDigits[n, 2]], 2] - FromDigits[ RotateLeft[ IntegerDigits[n, 2]], 2]; Table[ f[n], {n, 0, 82}]

Formula

a(n) = A038572(n) - A006257(n).