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A233263
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a(n) = prime(k), where k is such that (Sum_{j=1..k} prime(j)^12) / k is an integer.
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1
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2, 157, 72673, 52472909, 85790059, 88573873, 16903607381, 4582951241047, 162717490461611, 1220077659512857, 34871545949176799
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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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FORMULA
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EXAMPLE
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a(2) = 157, because 157 is the 37th prime and the sum of the first 37 primes^12 = 636533120636984811361212036 when divided by 37 equals 17203597855053643550303028 which is an integer.
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MAPLE
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MATHEMATICA
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t = {}; sm = 0; Do[sm = sm + Prime[n]^12; 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)^12); s==0 \\ Charles R Greathouse IV, Nov 30 2013
(PARI) S=n=0; forprime(p=1, , (S+=p^12)%n++||print1(p", ")) \\ M. F. Hasler, Dec 01 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,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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