%I #18 Apr 03 2023 10:36:12

%S 6,7,15,27,41,55,172,561,1334,6571,11490,429705,2173016,4417701,

%T 9063353,9531624,40411847,64538709,83537963,121316228,181504240,

%U 222586609

%N Natural numbers n such that Sum_{k = 1..pi(n)-1} p(k) == p(pi(n)) mod n, where p(k) denotes the k-th prime and pi(n) is the number of primes strictly less than n.

%H G. L. Honaker, Jr. and Chris Caldwell, <a href="https://t5k.org/curios/cpage/20463.html">Prime Curios! 6571</a>

%e 2+3+5+7+11==13 (mod 15) and so 15 has this property.

%t Reap[Module[{c = 0}, For[n = 4, n <= 10^6, n++, If[PrimeQ[n - 1], c += NextPrime[n - 1, -1]]; If[Mod[c, n] == NextPrime[n, -1], Sow[n]]]]]

%Y Cf. A000720.

%K nonn

%O 1,1

%A _Jake Foster_, Sep 29 2011