A102564 -id:A102564 - cp's OEIS frontend

A102565 a(n) = A102563(n) - A102564(n).

0, 0, 1, -2, 1, -2, -1, 0, 1, -2, -1, 0, -1, 0, 1, -2, 1, -2, -1, 0, -1, 0, 1, -2, -1, 0, 1, -2, 1, -2, -1, 0, 1, -2, -1, 0, -1, 0, 1, -2, -1, 0, 1, -2, 1, -2, -1, 0, -1, 0, 1, -2, 1, -2, -1, 0, 1, -2, -1, 0, -1, 0, 1, -2, 1, -2, -1, 0, -1, 0, 1, -2, -1, 0, 1, -2, 1, -2, -1, 0, -1, 0, 1, -2, 1, -2, -1, 0, 1, -2, -1, 0, -1, 0, 1, -2, -1, 0, 1, -2, 1

Offset: 0

Paul Barry, Jan 14 2005

It would appear that a(2n+1) = (-2)*A010060(n); a(4n+1) = (-2)*A010060(n); a(8n+1) = (-2)*A010060(n); a(2^n) = 0^n-1; a(2^n+1) = 3*0^n-2; a(2^(n+1)-1) = -(1-(-1)^n).

Cf. A010060, A076826, A102563, A102564.

A102563 a(n) = A000120(A001045(n)) - A001045(A000120(n)).

Original entry on oeis.org

0, 0, 0, 1, 1, 2, 2, 1, 3, 4, 4, 3, 5, 4, 4, 3, 7, 8, 8, 7, 9, 8, 8, 7, 11, 10, 10, 9, 11, 10, 10, 5, 15, 16, 16, 15, 17, 16, 16, 15, 19, 18, 18, 17, 19, 18, 18, 13, 23, 22, 22, 21, 23, 22, 22, 17, 25, 24, 24, 19, 25, 20, 20, 11, 31, 32, 32, 31, 33, 32, 32, 31, 35, 34, 34, 33, 35, 34

Offset: 0

Paul Barry, Jan 14 2005

Amiram Eldar, Table of n, a(n) for n = 0..10000

Cf. A000079, A000120, A000225, A001045, A102564, 102565.

j[n_] := (2^n - (-1)^n)/3; s[n_] := DigitCount[n, 2, 1]; a[n_] := s[j[n]] - j[s[n]]; Array[a, 100, 0] (* Amiram Eldar, Jul 22 2023 *)

It would appear that a(2^(n+1)) = A000225(n).
a(2^(n+1)-1) = A001045(n).
a(2^(n+1)+1) = A000079(n).
a(2n+1) = n; a(4n+1) - a(2n+1) = n; a(8n+1) - a(4n+1) = 2n; a(8n+1) - a(2n+1) = 3n.

cp's OEIS Frontend

A102565 a(n) = A102563(n) - A102564(n).

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A102563 a(n) = A000120(A001045(n)) - A001045(A000120(n)).

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