A083661 G.f.: 1/(1-x) * Sum_{k>=0} x^2^(k+2)/(1+x^2^k).

0, 0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 2, 1, 1, 0, 3, 2, 2, 1, 2, 1, 1, 0, 3, 2, 2, 1, 2, 1, 1, 0, 4, 3, 3, 2, 3, 2, 2, 1, 3, 2, 2, 1, 2, 1, 1, 0, 4, 3, 3, 2, 3, 2, 2, 1, 3, 2, 2, 1, 2, 1, 1, 0, 5, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 4, 3, 3, 2, 3, 2, 2, 1, 3, 2, 2, 1, 2, 1

Offset: 1

Author

Ralf Stephan, Jun 14 2003

Keywords

• nonn
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Ralf Stephan, Some divide-and-conquer sequences with (relatively) simple ordinary generating functions, 2004.
• Ralf Stephan, Table of generating functions.

Crossrefs

Cf. A000120, A023416, A079944, A080791.

Programs

Mathematica

a[n_] := DigitCount[n, 2, 0] + IntegerDigits[n, 2][[2]] - 1; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jul 16 2023 *)

PARI

for(n=1, 120, l=ceil(log(n)/log(2)); t=polcoeff(1/(1-x)*sum(k=0, l, (x^2^(k+2))/(1+x^2^k)) + O(x^(n+1)), n); print1(t", "))

Formula

a(1) = a(2) = a(3) = 0, a(2n) = a(n)+1, a(2n+1) = a(n).

a(n) = A080791(n) + A079944(n-2) - 1.