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A270828
a(n) = (Sum_{k=1..2n-1} prime(k)) mod prime(n).
1
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
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
KEYWORD
nonn
AUTHOR
Altug Alkan, Mar 23 2016
STATUS
approved