%I #11 May 14 2024 03:58:42
%S 8,17,53,69,76,84,87,91,167,175,179,181,188,196,201,217,219,224,240,
%T 260,275,297,312,317,319,324,340,346,376,382,386,393,417,470,503,514,
%U 526,528,542,550,562,564,584,590,607,613,615,629,637,649,691,693,732,749,752,759
%N Numbers k such that 11 divides prime(1) + ... + prime(k).
%H Michael S. Branicky, <a href="/A111325/b111325.txt">Table of n, a(n) for n = 1..10000</a>
%t Position[Accumulate[Prime[Range[400]]], _?(Divisible[#, 11] &)] // Flatten (* _Amiram Eldar_, May 14 2024 *)
%o (Python)
%o from sympy import nextprime
%o def aupto(limit):
%o p, s, alst = 2, 2, []
%o for k in range(1, limit+1):
%o if s == 0: alst.append(k)
%o p = nextprime(p); s = (s + p)%11
%o return alst
%o print(aupto(759)) # _Michael S. Branicky_, Aug 17 2021
%o (PARI) lista(pmax) = {my(s = 0, k = 0); forprime(p = 2, pmax, k++; s += p; if(!(s % 11), print1(k, ", ")));} \\ _Amiram Eldar_, May 14 2024
%Y Cf. A007504, A103208, A111318, A111319, A111320, A111321, A111322, A111323, A111324, A111326, A111327.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Nov 05 2005