A278743 - cp's OEIS frontend

A278743 For a base n>1: consider the lexicographically least strictly increasing sequence c_n such that, for any m>0, Sum_{k=1..m} c_n(k) can be computed without carries in base n; the sequence c_n is (conjecturally) eventually linear, and a(n) gives its order.

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

[1, 3, 2, 5, 9, 3, 7, 4, 17, 4, 9, 15, 21, 11, 5, 11, 25, 25, 13, 7, 6, 13, 7, 29, 15, 16, 25, 7, 15, 9, 33, 17, 10, 28, 57, 8, 17, 49, 37, 19, 10, 31, 63, 21, 9, 19, 43, 41, 21, 34, 34, 69, 23, 12, 10, 21, 13, 45, 23, 51, 37, 75, 25, 13, 67, 11, 23, 42, 49, 25]

cp's OEIS Frontend

A278743 For a base n>1: consider the lexicographically least strictly increasing sequence c_n such that, for any m>0, Sum_{k=1..m} c_n(k) can be computed without carries in base n; the sequence c_n is (conjecturally) eventually linear, and a(n) gives its order.

Table of values

List of values

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

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

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