# [seqfan] A178215, A178216

Vladimir Shevelev shevelev at bgu.ac.il
Sat May 22 23:15:14 CEST 2010

```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)
%e A178215 If n=3, then p_n=5 and we see that {2,3,5,7,11,13,17,19} is the minimal set of the first primes, which contains all residues modulo 5 (we have consecutive residues {2,3,0,2,1,3,2,4}. Therefore, a(3)=8.
%Y A178215 A000040
%K A178215 nonn
%O A178215 1,1

and

%I A178216
%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.
%e A178216 If n=3, then p_n=5 and {2,3,5,7,11,13,17,19} is the minimal set of the first primes, which contains all residues modulo 5. We have consecutive residues {2,3,0,2,1,3,2,4}. Therefore, a(3)=4.
%Y A178216 A000040 A178215
%K A178216 nonn
%O A178216 1,3

It seems that in A178216  repeat often 1 and p-1(?) Can anyone extend these sequences?

Best regards,
Vladimir

Shevelev Vladimir‎

```

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