A137605 - cp's OEIS frontend

A137605 Consider the sequence: b(0) = n, and for k >= 1, b(k) = b(k-1)/2 if b(k-1) is even, otherwise b(k) = n - (b(k-1)+1)/2. Then a(n) = m, where m is the smallest index such that b(m) = 1.

n	a(n)
1	0
2	1
3	1
4	2
5	2
6	4
7	5
8	3
9	3
10	8
11	5
12	10
13	9
14	8
15	13
16	4
17	4
18	11
19	17
20	11
21	9
22	6
23	11
24	22
25	20
26	7
27	25
28	19
29	8
30	28
31	29
32	5
33	5
34	32
35	21
36	34
37	8
38	19
39	29
40	38
41	26
42	40
43	7
44	27
45	10
46	11
47	9
48	35
49	23
50	14
51	49
52	50
53	11
54	52
55	17
56	35
57	13
58	43
59	11
60	23
61	54
62	19
63	49
64	6
65	6
66	64
67	17
68	35
69	33
70	68
71	45
72	59
73	13
74	41
75	73
76	14
77	23
78	19
79	25

[0, 1, 1, 2, 2, 4, 5, 3, 3, 8, 5, 10, 9, 8, 13, 4, 4, 11, 17, 11, 9, 6, 11, 22, 20, 7, 25, 19, 8, 28, 29, 5, 5, 32, 21, 34, 8, 19, 29, 38, 26, 40, 7, 27, 10, 11, 9, 35, 23, 14, 49, 50, 11, 52, 17, 35, 13, 43, 11, 23, 54, 19, 49, 6, 6, 64, 17, 35, 33, 68, 45, 59, 13, 41, 73, 14, 23, 19, 25]

cp's OEIS Frontend

A137605 Consider the sequence: b(0) = n, and for k >= 1, b(k) = b(k-1)/2 if b(k-1) is even, otherwise b(k) = n - (b(k-1)+1)/2. Then a(n) = m, where m is the smallest index such that b(m) = 1.

Table of values

List of values

n	a(n)
1	0
2	1
3	1
4	2
5	2
6	4
7	5
8	3
9	3
10	8
11	5
12	10
13	9
14	8
15	13
16	4
17	4
18	11
19	17
20	11
21	9
22	6
23	11
24	22
25	20
26	7
27	25
28	19
29	8
30	28
31	29
32	5
33	5
34	32
35	21
36	34
37	8
38	19
39	29
40	38
41	26
42	40
43	7
44	27
45	10
46	11
47	9
48	35
49	23
50	14
51	49
52	50
53	11
54	52
55	17
56	35
57	13
58	43
59	11
60	23
61	54
62	19
63	49
64	6
65	6
66	64
67	17
68	35
69	33
70	68
71	45
72	59
73	13
74	41
75	73
76	14
77	23
78	19
79	25

n	a(n)
1	0
2	1
3	1
4	2
5	2
6	4
7	5
8	3
9	3
10	8
11	5
12	10
13	9
14	8
15	13
16	4
17	4
18	11
19	17
20	11
21	9
22	6
23	11
24	22
25	20
26	7
27	25
28	19
29	8
30	28
31	29
32	5
33	5
34	32
35	21
36	34
37	8
38	19
39	29
40	38
41	26
42	40
43	7
44	27
45	10
46	11
47	9
48	35
49	23
50	14
51	49
52	50
53	11
54	52
55	17
56	35
57	13
58	43
59	11
60	23
61	54
62	19
63	49
64	6
65	6
66	64
67	17
68	35
69	33
70	68
71	45
72	59
73	13
74	41
75	73
76	14
77	23
78	19
79	25

n	a(n)
1	0
2	1
3	1
4	2
5	2
6	4
7	5
8	3
9	3
10	8
11	5
12	10
13	9
14	8
15	13
16	4
17	4
18	11
19	17
20	11
21	9
22	6
23	11
24	22
25	20
26	7
27	25
28	19
29	8
30	28
31	29
32	5
33	5
34	32
35	21
36	34
37	8
38	19
39	29
40	38
41	26
42	40
43	7
44	27
45	10
46	11
47	9
48	35
49	23
50	14
51	49
52	50
53	11
54	52
55	17
56	35
57	13
58	43
59	11
60	23
61	54
62	19
63	49
64	6
65	6
66	64
67	17
68	35
69	33
70	68
71	45
72	59
73	13
74	41
75	73
76	14
77	23
78	19
79	25