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A233769
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Prime(k), where k is such that (1 + Sum_{i=1..k} prime(i)^19) / k is an integer.
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1
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2, 3, 7, 11, 13, 29, 37, 241, 1429, 2437, 2741, 4583, 7333, 8269, 36073, 37397, 48121, 73037, 130261, 147289, 280037, 1032259, 6594787, 10249573, 130193849, 443038781, 527454197, 1024907927, 1736090963, 2602512709, 13517865841, 13684220029, 64209198247, 93380481511, 126718347859, 143176188581, 231059158871, 273286859737, 511940464493, 512760363097, 715173864563, 810985955573
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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13 is a term, because 13 is the 6th prime and the sum of the first 6 primes^19+1 = 1523090798793695143992 when divided by 6 equals 253848466465615857332 which is an integer.
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MATHEMATICA
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t = {}; sm = 1; Do[sm = sm + Prime[n]^19; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
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PROG
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(PARI) is(n)=if(!isprime(n), return(0)); my(t=primepi(n), s); forprime(p=2, n, s+=Mod(p, t)^19); s==0 \\ Charles R Greathouse IV, Nov 30 2013
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CROSSREFS
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Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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