A099033 - OEIS

%I #11 Jan 03 2018 14:55:40

%S 1,2,3,4,5,6,5,6,7,8,9,10,11,10,11,12,13,14,15,16,17,18,17,18,19,20,

%T 19,18,17,18,17,18,19,20,21,22,23,24,23,24,25,26,27,28,29,28,29,30,31,

%U 32,33,34,35,34,35,34,33,32,33,34,35,34,35,36,37,38,39,40,41,42,41,42

%N a(n) = Sum_{k=1..n} (-1)^A000120(3*k).

%C a(n) is of order n^log4(3).

%H G. C. Greubel, <a href="/A099033/b099033.txt">Table of n, a(n) for n = 1..1000</a>

%H P. 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.

%t A036555 := Total /@ IntegerDigits[3 Range[1, 130], 2]; Table[Sum[ (-1)^A036555[[k]], {k, 1, n}], {n, 1, 50}] (* _G. C. Greubel_, Jan 01 2017 *)

%o (PARI) a(n) = sum(k=1, n, (-1)^hammingweight(3*k)); \\ _Michel Marcus_, Dec 03 2016

%Y Cf. A000120, A036555.

%K nonn

%O 1,2

%A _Ralf Stephan_, Sep 27 2004

%E Typo in name corrected by _Michel Marcus_, Dec 03 2016