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Numbers k such that 13 divides prime(1) + ... + prime(k).
11

%I #8 May 14 2024 03:58:36

%S 49,61,67,87,92,117,119,126,131,160,166,179,203,253,269,295,297,299,

%T 319,344,348,360,381,393,408,418,429,437,442,451,485,496,502,506,508,

%U 510,532,541,553,559,565,585,591,623,626,647,652,656,662,672,692,712,715,733,736

%N Numbers k such that 13 divides prime(1) + ... + prime(k).

%H Amiram Eldar, <a href="/A111327/b111327.txt">Table of n, a(n) for n = 1..10000</a>

%t Position[Accumulate[Prime[Range[400]]], _?(Divisible[#, 13] &)] // Flatten (* _Amiram Eldar_, May 14 2024 *)

%o (PARI) lista(pmax) = {my(s = 0, k = 0); forprime(p = 2, pmax, k++; s += p; if(!(s % 13), print1(k, ", ")));} \\ _Amiram Eldar_, May 14 2024

%Y Cf. A007504, A103208, A111318, A111319, A111320, A111321, A111322, A111323, A111324, A111325, A111326.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Nov 05 2005