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

1,3

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

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A000040, A007504, A109723.

Sequence in context: A111572 A046900 A365367 * A325315 A230845 A194528

Adjacent sequences: A270825 A270826 A270827 * A270829 A270830 A270831

Keyword

nonn

Author

Altug Alkan, Mar 23 2016

Status

approved