A342697 - cp's OEIS frontend

A342697 For any number n with binary expansion Sum_{k >= 0} b(k) * 2^k, the binary expansion of a(n) is Sum_{k >= 0} floor((b(k) + b(k+1) + b(k+2))/2) * 2^k.

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

[0, 0, 0, 1, 0, 1, 3, 3, 0, 0, 2, 3, 6, 7, 7, 7, 0, 0, 0, 1, 4, 5, 7, 7, 12, 12, 14, 15, 14, 15, 15, 15, 0, 0, 0, 1, 0, 1, 3, 3, 8, 8, 10, 11, 14, 15, 15, 15, 24, 24, 24, 25, 28, 29, 31, 31, 28, 28, 30, 31, 30, 31, 31, 31, 0, 0, 0, 1, 0, 1, 3, 3, 0, 0, 2, 3, 6]

cp's OEIS Frontend

A342697 For any number n with binary expansion Sum_{k >= 0} b(k) * 2^k, the binary expansion of a(n) is Sum_{k >= 0} floor((b(k) + b(k+1) + b(k+2))/2) * 2^k.

Table of values

List of values

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

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

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