A196223 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..22.

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

EXAMPLE

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

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]]]]]

CROSSREFS

Cf. A000720.