A270828 a(n) = (Sum_{k=1..2n-1} prime(k)) mod prime(n).

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, 62, 25, 3, 73, 108, 67, 27, 124, 108, 66, 34, 4, 130, 102, 80, 40, 32, 169, 132, 78, 79, 128, 75, 5, 215, 227, 189, 243, 255, 259, 261, 193, 197, 162, 98, 148, 9, 281, 213, 194, 87, 109, 261, 171

Offset: 1

Author

Altug Alkan, Mar 23 2016

Keywords

• nonn

Comments

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

No other zero up to n=200000. - Michel Marcus, Jan 31 2019

Examples

			a(2) = 1 because (2 + 3 + 5) mod 3 = 1.
a(7) = 0 because (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41) mod 17 = 238 mod 17 = 0.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A007504, A109723.

Programs

Mathematica

Table[Mod[Sum[Prime@ k, {k, 2 n - 1}], Prime@ n], {n, 70}] (* Michael De Vlieger, Mar 24 2016 *)

PARI

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

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

Formula

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