cp's OEIS Frontend

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

%I A099034 #20 Jul 18 2023 02:28:33
%S A099034 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,
%T A099034 11,12,13,14,13,14,15,14,13,14,15,14,15,14,15,16,17,18,19,20,19,20,21,
%U A099034 20,19,18,17,18,19,18,19,20,21,22,23,24,23,24,23,24,25,24,23
%N A099034 a(n) = Sum_{k=1..n} (-1)^A000120(5*k).
%H A099034 Gheorghe Coserea, <a href="/A099034/b099034.txt">Table of n, a(n) for n = 1..65536</a>
%H A099034 Peter J. Grabner, <a href="http://www.mat.univie.ac.at/~slc/opapers/s30grabner.html">A note on the parity of the sum-of-digits function</a>, Séminaire Lotharingien de Combinatoire, B30e (1993), 8 pp.
%F A099034 a(n) is of order n^(log(5)/log(16)).
%F A099034 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
%t A099034 Accumulate[(-1)^Array[DigitCount[5*#, 2, 1] &, 100]] (* _Amiram Eldar_, Jul 18 2023 *)
%o A099034 (PARI) a(n) = sum(k=1, n, (-1)^hammingweight(5*k));
%o A099034 (PARI)
%o A099034 seq(N) = {
%o A099034   my(v = vector(N), w=0); v[1] = 1;
%o A099034   for (k = 2, N, w = hammingweight(5*k)%2; v[k] = v[k-1] + 1-2*w);
%o A099034   v;
%o A099034 };
%o A099034 seq(75) \\ _Gheorghe Coserea_, Dec 03 2016
%Y A099034 Cf. A000120, A046820, A099033.
%K A099034 nonn,base
%O A099034 1,2
%A A099034 _Ralf Stephan_, Sep 27 2004
%E A099034 Name corrected by _Michel Marcus_, Dec 03 2016