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 A233523 Prime(n), where n is such that (1+sum_{i=1..n} prime(i)) / n is an integer. 91
 2, 3, 13, 29, 71, 79, 107, 907, 3491, 4967, 7853, 61223, 80051, 81547, 90901, 211811, 381629, 1990007, 3220793, 4749637, 6725027, 6784937, 34463699, 143691323, 185831033, 213609173, 285336497, 442634651, 911588849, 953122843, 1548789581, 2153787017 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(44) > 1177154790607. LINKS Robert Price, Table of n, a(n) for n = 1..43 EXAMPLE a(3) = 13, because 13 is the 6th prime and the sum of the first 6 primes+1 = 42 when divided by 6 equals 7 which is an integer. MATHEMATICA t = {}; sm = 1; Do[sm = sm + Prime[n]; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *) PROG (PARI) is(n)=if(!isprime(n), return(0)); my(t=primepi(n), s); forprime(p=2, n, s+=Mod(p, t)); s==0 \\ Charles R Greathouse IV, Nov 30 2013 CROSSREFS Cf. A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n. Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248. Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601. Sequence in context: A141861 A215379 A215375 * A256712 A092175 A317898 Adjacent sequences:  A233520 A233521 A233522 * A233524 A233525 A233526 KEYWORD nonn AUTHOR Robert Price, Dec 15 2013 STATUS approved

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Last modified August 4 02:10 EDT 2020. Contains 336201 sequences. (Running on oeis4.)