A348691 - cp's OEIS frontend

A348691 For any nonnegative number n with binary expansion Sum_{k >= 0} b_k * 2^k, a(n) is the imaginary part of f(n) = Sum_{k >= 0} b_k * (i^Sum_{j = 0..k-1} b_j) * (1+i)^k (where i denotes the imaginary unit); sequence A348690 gives the real part.

n	a(n)
0	0
1	0
2	1
3	1
4	2
5	0
6	1
7	-1
8	2
9	-2
10	-1
11	-1
12	0
13	-2
14	-1
15	1
16	0
17	-4
18	-3
19	1
20	-2
21	0
22	1
23	3
24	-2
25	-2
26	-1
27	3
28	0
29	2
30	3
31	1
32	-4
33	-4
34	-3
35	5
36	-2
37	4
38	5
39	3
40	-2
41	2
42	3
43	3
44	4
45	2
46	3
47	-3
48	-4
49	0
50	1
51	5
52	2
53	4
54	5
55	-1
56	2
57	2
58	3
59	-1
60	4
61	-2
62	-1
63	-3
64	-8
65	0
66	1
67	9
68	2
69	8
70	9
71	-1
72	2
73	6
74	7
75	-1
76	8
77	-2

[0, 0, 1, 1, 2, 0, 1, -1, 2, -2, -1, -1, 0, -2, -1, 1, 0, -4, -3, 1, -2, 0, 1, 3, -2, -2, -1, 3, 0, 2, 3, 1, -4, -4, -3, 5, -2, 4, 5, 3, -2, 2, 3, 3, 4, 2, 3, -3, -4, 0, 1, 5, 2, 4, 5, -1, 2, 2, 3, -1, 4, -2, -1, -3, -8, 0, 1, 9, 2, 8, 9, -1, 2, 6, 7, -1, 8, -2]

cp's OEIS Frontend

A348691 For any nonnegative number n with binary expansion Sum_{k >= 0} b_k * 2^k, a(n) is the imaginary part of f(n) = Sum_{k >= 0} b_k * (i^Sum_{j = 0..k-1} b_j) * (1+i)^k (where i denotes the imaginary unit); sequence A348690 gives the real part.

Table of values

List of values

n	a(n)
0	0
1	0
2	1
3	1
4	2
5	0
6	1
7	-1
8	2
9	-2
10	-1
11	-1
12	0
13	-2
14	-1
15	1
16	0
17	-4
18	-3
19	1
20	-2
21	0
22	1
23	3
24	-2
25	-2
26	-1
27	3
28	0
29	2
30	3
31	1
32	-4
33	-4
34	-3
35	5
36	-2
37	4
38	5
39	3
40	-2
41	2
42	3
43	3
44	4
45	2
46	3
47	-3
48	-4
49	0
50	1
51	5
52	2
53	4
54	5
55	-1
56	2
57	2
58	3
59	-1
60	4
61	-2
62	-1
63	-3
64	-8
65	0
66	1
67	9
68	2
69	8
70	9
71	-1
72	2
73	6
74	7
75	-1
76	8
77	-2

n	a(n)
0	0
1	0
2	1
3	1
4	2
5	0
6	1
7	-1
8	2
9	-2
10	-1
11	-1
12	0
13	-2
14	-1
15	1
16	0
17	-4
18	-3
19	1
20	-2
21	0
22	1
23	3
24	-2
25	-2
26	-1
27	3
28	0
29	2
30	3
31	1
32	-4
33	-4
34	-3
35	5
36	-2
37	4
38	5
39	3
40	-2
41	2
42	3
43	3
44	4
45	2
46	3
47	-3
48	-4
49	0
50	1
51	5
52	2
53	4
54	5
55	-1
56	2
57	2
58	3
59	-1
60	4
61	-2
62	-1
63	-3
64	-8
65	0
66	1
67	9
68	2
69	8
70	9
71	-1
72	2
73	6
74	7
75	-1
76	8
77	-2

n	a(n)
0	0
1	0
2	1
3	1
4	2
5	0
6	1
7	-1
8	2
9	-2
10	-1
11	-1
12	0
13	-2
14	-1
15	1
16	0
17	-4
18	-3
19	1
20	-2
21	0
22	1
23	3
24	-2
25	-2
26	-1
27	3
28	0
29	2
30	3
31	1
32	-4
33	-4
34	-3
35	5
36	-2
37	4
38	5
39	3
40	-2
41	2
42	3
43	3
44	4
45	2
46	3
47	-3
48	-4
49	0
50	1
51	5
52	2
53	4
54	5
55	-1
56	2
57	2
58	3
59	-1
60	4
61	-2
62	-1
63	-3
64	-8
65	0
66	1
67	9
68	2
69	8
70	9
71	-1
72	2
73	6
74	7
75	-1
76	8
77	-2