A111325 Numbers k such that 11 divides prime(1) + ... + prime(k).

8, 17, 53, 69, 76, 84, 87, 91, 167, 175, 179, 181, 188, 196, 201, 217, 219, 224, 240, 260, 275, 297, 312, 317, 319, 324, 340, 346, 376, 382, 386, 393, 417, 470, 503, 514, 526, 528, 542, 550, 562, 564, 584, 590, 607, 613, 615, 629, 637, 649, 691, 693, 732, 749, 752, 759

Offset: 1

Author

N. J. A. Sloane, Nov 05 2005

Keywords

• nonn

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007504, A103208, A111318, A111319, A111320, A111321, A111322, A111323, A111324, A111326, A111327.

Programs

Mathematica

Position[Accumulate[Prime[Range[400]]], ?(Divisible[#, 11] &)] // Flatten (* _Amiram Eldar, May 14 2024 *)

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

Python

from sympy import nextprime
def aupto(limit):
    p, s, alst = 2, 2, []
    for k in range(1, limit+1):
        if s == 0: alst.append(k)
        p = nextprime(p); s = (s + p)%11
    return alst
print(aupto(759)) # Michael S. Branicky, Aug 17 2021