# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a270828 Showing 1-1 of 1 %I A270828 #20 Jan 31 2019 03:28:26 %S A270828 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 A270828 62,25,3,73,108,67,27,124,108,66,34,4,130,102,80,40,32,169,132,78,79, %U A270828 128,75,5,215,227,189,243,255,259,261,193,197,162,98,148,9,281,213,194,87,109,261,171 %N A270828 a(n) = (Sum_{k=1..2n-1} prime(k)) mod prime(n). %C A270828 a(n) = 0 for n = 1, 7, 100. Are there any other values? %C A270828 No other zero up to n=200000. - _Michel Marcus_, Jan 31 2019 %H A270828 Michel Marcus, Table of n, a(n) for n = 1..10000 %F A270828 a(n) = A007504(2*n-1) mod A000040(n). %e A270828 a(2) = 1 because (2 + 3 + 5) mod 3 = 1. %e A270828 a(7) = 0 because (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41) mod 17 = 238 mod 17 = 0. %t A270828 Table[Mod[Sum[Prime@ k, {k, 2 n - 1}], Prime@ n], {n, 70}] (* _Michael De Vlieger_, Mar 24 2016 *) %o A270828 (PARI) for(n=1, 1e2, print1(sum(k=1, 2*n-1, prime(k)) % prime(n), ", ")); %o A270828 (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 A270828 Cf. A000040, A007504, A109723. %K A270828 nonn %O A270828 1,3 %A A270828 _Altug Alkan_, Mar 23 2016 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE