

A099034


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


1



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
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OFFSET

1,2


COMMENTS

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


LINKS

Gheorghe Coserea, Table of n, a(n) for n = 1..65536
P. J. Grabner, A note on the parity of the sumofdigits function, SÃ©minaire Lotharingien de Combinatoire, B30e (1993), 8 pp.


FORMULA

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


PROG

(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[k1] + 12*w);
v;
};
seq(75) \\ Gheorghe Coserea, Dec 03 2016


CROSSREFS

Cf. A046820, A099033.
Sequence in context: A123709 A165482 A323242 * A165576 A304730 A323374
Adjacent sequences: A099031 A099032 A099033 * A099035 A099036 A099037


KEYWORD

nonn,base


AUTHOR

Ralf Stephan, Sep 27 2004


EXTENSIONS

Name corrected by Michel Marcus, Dec 03 2016


STATUS

approved



