[seqfan] Re: A178215, A178216

[Vladimir Shevelev]

Very thanks, Doug!

Vladimir

----- Original Message -----
From: Douglas McNeil <mcneil at hku.hk>
Date: Sunday, May 23, 2010 9:38
Subject: [seqfan] Re: A178215, A178216
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>

> 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
> 
> 
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 Shevelev Vladimir‎