A196223 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.

6, 7, 15, 27, 41, 55, 172, 561, 1334, 6571, 11490, 429705, 2173016, 4417701, 9063353, 9531624, 40411847, 64538709, 83537963, 121316228, 181504240, 222586609

Offset: 1

Author

Jake Foster, Sep 29 2011

Keywords

• nonn

Examples

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

Links

• G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 6571

Crossrefs

Cf. A000720.

Programs

Mathematica

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]]]]]