A111320 Numbers k such that 6 divides prime(1) + ... + prime(k).

57, 97, 99, 103, 105, 107, 111, 113, 119, 121, 123, 125, 127, 129, 161, 163, 169, 175, 177, 179, 185, 187, 195, 197, 199, 203, 205, 207, 211, 213, 217, 233, 235, 237, 273, 293, 295, 297, 301, 303, 305, 307, 309, 311, 327, 329, 331, 333, 335, 337, 339, 343, 345, 347, 349

Offset: 1

Author

N. J. A. Sloane, Nov 05 2005

Keywords

• nonn

Comments

Odd terms in A103208. - Robert Israel, Jan 26 2019

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007504, A103208, A111318, A111319, A111321, A111322, A111323, A111324, A111325, A111326, A111327.

Programs

Maple

P:= [seq(ithprime(i),i=1..1000)]:
L:= ListTools:-PartialSums(P):
select(t -> L[t] mod 6 = 0, [seq(i,i=1..1000)]); # Robert Israel, Jan 26 2019

Mathematica

Position[Accumulate[Prime[Range[400]]], ?(Divisible[#, 6] &)] // Flatten (* _Amiram Eldar, May 14 2024 *)

PARI

lista(pmax) = {my(s = 0, k = 0); forprime(p = 2, pmax, k++; s += p; if(!(s % 6), print1(k, ", ")));} \\ Amiram Eldar, May 14 2024