|
| |
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
LINKS
|
|
|
|
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
|
|
|
MATHEMATICA
|
Accumulate[(-1)^Array[DigitCount[5*#, 2, 1] &, 100]] (* Amiram Eldar, Jul 18 2023 *)
|
|
|
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[k-1] + 1-2*w);
v;
};
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,base
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
