A099034 a(n) = Sum_{k=1..n} (-1)^A000120(5*k).

1, 2, 3, 4, 3, 4, 3, 4, 5, 4, 3, 4, 5, 4, 5, 6, 7, 8, 9, 8, 9, 8, 7, 8, 9, 10, 11, 10, 9, 10, 9, 10, 11, 12, 13, 14, 13, 14, 15, 14, 13, 14, 15, 14, 15, 14, 15, 16, 17, 18, 19, 20, 19, 20, 21, 20, 19, 18, 17, 18, 19, 18, 19, 20, 21, 22, 23, 24, 23, 24, 23, 24, 25, 24, 23

Offset: 1

Author

Ralf Stephan, Sep 27 2004

Keywords

• nonn
• base

Links

• Gheorghe Coserea, Table of n, a(n) for n = 1..65536
• Peter J. Grabner, A note on the parity of the sum-of-digits function, Séminaire Lotharingien de Combinatoire, B30e (1993), 8 pp.

Crossrefs

Cf. A000120, A046820, A099033.

Programs

Mathematica

Accumulate[(-1)^Array[DigitCount[5*#, 2, 1] &, 100]] (* Amiram Eldar, Jul 18 2023 *)

PARI

a(n) = sum(k=1, n, (-1)^hammingweight(5*k));

PARI

seq(N) = {
  my(v = vector(N), w=0); v[1] = 1;
  for (k = 2, N, w = hammingweight(5*k)%2; v[k] = v[k-1] + 1-2*w);
  v;
};
seq(75) \\ Gheorghe Coserea, Dec 03 2016

Formula

a(n) is of order n^(log(5)/log(16)).

a(2*16^n) = 2*5^n, a(4*16^n) = a(8*16^n) = 4*5^n, a(16^(n+1)) = 6*5^n. - Gheorghe Coserea, Dec 03 2016

Extensions

Name corrected by Michel Marcus, Dec 03 2016