# [seqfan] Re: A178215, A178216

Douglas McNeil mcneil at hku.hk
Sun May 23 08:15:19 CEST 2010

```On Sun, May 23, 2010 at 5:15 AM, Vladimir Shevelev <shevelev at bgu.ac.il> wrote:
> Dear seqfans,
>
> i have just submitted two sequences:
>
> %I A178215
> %S A178215 2,4,8,10,14,27,27,43,33,76
> %N A178215 a(n) is the least number such that the set {p_1,p_2,...,p_a(n)} contains all residues modulo p_n (p_m is m-th prime)

> %S A178216 1,1,4,1,10,12,1,1,22,6
> %N A178216 a(n)==p_(A178215(n)) mod p_n (0<=a(n)<=p_n-1)
> %C A178216 a(n) is the last residue modulo p_n in the minimal set of the first primes, which contains all residues modulo p_n.

I differ on a(10) for both sequences:

sage: A178215
[2, 4, 8, 10, 14, 27, 27, 43, 33, 66, 64, 85, 75, 90, 163, 111, 127,
178, 170, 145, 172, 215, 197, 238, 239, 324, 298, 364, 345, 328, 516,
442, 544, 421, 482, 613, 495, 605, 544, 647, 553, 646, 645, 520, 743,
594, 738, 645, 852, 1013, 788, 1205, 728, 900, 801, 1047, 994, 957,
1007, 1030, 1552, 1095, 1241, 1318, 1417, 1450, 1280, 2009, 1618,
1898, 1574, 1197, 1388, 1587, 1454, 1356, 1398, 1736, 1686, 2683,
1464, 1779, 1873, 1688, 1597, 1606, 2134, 1622, 3957, 2717, 1703,
1955, 1554, 2358, 1961, 2066, 1790, 2645, 2766]
sage: A178216
[1, 1, 4, 1, 10, 12, 1, 1, 22, 27, 1, 32, 10, 33, 27, 24, 1, 24, 8,
48, 72, 55, 39, 69, 44, 22, 16, 105, 44, 56, 14, 76, 87, 129, 22, 138,
85, 50, 82, 130, 69, 93, 18, 60, 135, 170, 105, 110, 225, 44, 218,
209, 205, 220, 232, 210, 72, 230, 237, 70, 15, 286, 279, 273, 240, 63,
198, 284, 158, 309, 180, 4, 126, 326, 21, 90, 340, 132, 354, 385, 100,
85, 144, 118, 299, 287, 282, 1, 22, 405, 66, 178, 381, 341, 45, 436,
49, 328, 456]

> It seems that in A178216  repeat often 1 and p-1(?)

1 doesn't seem to show up that often, but more often than anything else.

Doug

--
Department of Earth Sciences
University of Hong Kong

```