|
|
A318703
|
|
For any n >= 0 with binary expansion Sum_{k=0..w} b_k * 2^k, let f(n) = Sum_{k=0..w} b_k * i^k * 2^floor(k/2) (where i denotes the imaginary unit); a(n) is the imaginary part of f(n).
|
|
3
|
|
|
0, 0, 1, 1, 0, 0, 1, 1, -2, -2, -1, -1, -2, -2, -1, -1, 0, 0, 1, 1, 0, 0, 1, 1, -2, -2, -1, -1, -2, -2, -1, -1, 4, 4, 5, 5, 4, 4, 5, 5, 2, 2, 3, 3, 2, 2, 3, 3, 4, 4, 5, 5, 4, 4, 5, 5, 2, 2, 3, 3, 2, 2, 3, 3, 0, 0, 1, 1, 0, 0, 1, 1, -2, -2, -1, -1, -2, -2, -1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,9
|
|
COMMENTS
|
See A318702 for the real part of f and additional comments.
|
|
LINKS
|
|
|
FORMULA
|
a(2*n) = a(2*n + 1) for any n >= 0.
a(4 * k) = -2 * a(k) for any k >= 0.
|
|
MATHEMATICA
|
Array[Im[Total@ MapIndexed[#1*I^(First@ #2 - 1)*2^Floor[(First@ #2 - 1)/2] &, Reverse@ IntegerDigits[#, 2]]] &, 75, 0] (* Michael De Vlieger, Sep 02 2018 *)
|
|
PROG
|
(PARI) a(n) = my (b=Vecrev(binary(n))); imag(sum(k=1, #b, b[k] * I^(k-1) * 2^floor((k-1)/2)))
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|