%I #20 Jan 31 2019 03:28:26

%S 0,1,3,2,1,4,0,5,3,17,30,23,35,17,23,24,41,19,38,3,54,4,44,77,38,98,

%T 62,25,3,73,108,67,27,124,108,66,34,4,130,102,80,40,32,169,132,78,79,

%U 128,75,5,215,227,189,243,255,259,261,193,197,162,98,148,9,281,213,194,87,109,261,171

%N a(n) = (Sum_{k=1..2n-1} prime(k)) mod prime(n).

%C a(n) = 0 for n = 1, 7, 100. Are there any other values?

%C No other zero up to n=200000. - _Michel Marcus_, Jan 31 2019

%H Michel Marcus, <a href="/A270828/b270828.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A007504(2*n-1) mod A000040(n).

%e a(2) = 1 because (2 + 3 + 5) mod 3 = 1.

%e a(7) = 0 because (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41) mod 17 = 238 mod 17 = 0.

%t Table[Mod[Sum[Prime@ k, {k, 2 n - 1}], Prime@ n], {n, 70}] (* _Michael De Vlieger_, Mar 24 2016 *)

%o (PARI) for(n=1, 1e2, print1(sum(k=1, 2*n-1, prime(k)) % prime(n), ", "));

%o (PARI) lista(nn) = {my(s=0, p=1); for (n=1, nn, p = nextprime(p+1); s += p; print1(s % prime(n), ", "); p = nextprime(p+1); s += p;);} \\ _Michel Marcus_, Jan 31 2019

%Y Cf. A000040, A007504, A109723.

%K nonn

%O 1,3

%A _Altug Alkan_, Mar 23 2016