|
| |
|
|
A368595
|
|
Alternating sum of A006519.
|
|
1
|
|
|
|
-1, 1, 0, 4, 3, 5, 4, 12, 11, 13, 12, 16, 15, 17, 16, 32, 31, 33, 32, 36, 35, 37, 36, 44, 43, 45, 44, 48, 47, 49, 48, 80, 79, 81, 80, 84, 83, 85, 84, 92, 91, 93, 92, 96, 95, 97, 96, 112, 111, 113, 112, 116, 115, 117, 116, 124, 123, 125, 124, 128, 127, 129, 128
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,4
|
|
|
COMMENTS
|
a(n) <= (n/2)*log_2 n, with equality at powers of 2.
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n) = Sum_{i=1..n} (-1)^i*A006519(i).
|
|
|
MATHEMATICA
|
a[1]=-1; a[n_]:=If[OddQ[n], a[n-1]-2^IntegerExponent[n, 2], a[n-1]+2^IntegerExponent[n, 2]]; Table[a[n], {n, 63}] (* James C. McMahon, Dec 31 2023 *)
|
|
|
PROG
|
(PARI) a(n) = fromdigits(Vec(Pol(binary(n))'), 2) - bitand(n, 1); \\ Kevin Ryde, Jan 01 2024
(Python)
def A368595(n): return sum(map(lambda x:(x[0]+1)*(1<<x[0]), filter(lambda x:x[1]=='1', enumerate(bin(n)[-2:1:-1]))))-(n&1) # Chai Wah Wu, Jan 01 2024
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
sign,easy
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
