A088172 First differences of A019300.

1, 2, 3, 7, 13, 26, 53, 106, 211, 422, 845, 1689, 3379, 6758, 13515, 27031, 54061, 108122, 216245, 432489, 864979, 1729958, 3459915, 6919830, 13839661, 27679322, 55358643, 110717287, 221434573, 442869146, 885738293, 1771476586, 3542953171

Offset: 1

Author

Gary W. Adamson, Sep 21 2003

Keywords

• nonn

Comments

Partial sums give A019300, while partial sums mod 2 = the Thue-Morse sequence, A010060. a(n) mod 2 = A035263: 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, ...

Crossrefs

Cf. A019300, A010060, A035263.

Programs

Mathematica

tm = Table[ If[ OddQ[ Count[ IntegerDigits[n, 2], 1]], 1, 0], {n, 0, 35}]; Table[ FromDigits[ Take[ tm, n + 1], 2] - FromDigits[ Take[ tm, n], 2], {n, 1, 33}] (* Robert G. Wilson v *)

Formula

a(n+1) = 2*a(n) + 0 or +-1. - Robert G. Wilson v, Sep 27 2003

a(n+1) = 2*a(n) + A029883(n). - Philippe Deléham, Mar 21 2004

Extensions

More terms from Robert G. Wilson v, Sep 27 2003