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A109628
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Numbers k such that the numerator of Sum_{i=1..k} 1/prime(i), in reduced form, is prime.
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7
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2, 3, 5, 6, 18, 19, 22, 47, 57, 58, 63, 70, 73, 112, 632, 1382
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OFFSET
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1,1
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COMMENTS
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Terms <= 112 correspond to certified primes.
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LINKS
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EXAMPLE
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Sum_{i=1..6} 1/prime(i) = 40361/30030 and 40361 is prime, hence 6 is a term.
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MATHEMATICA
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s = 0; Do[s += 1/Prime[n]; k = Numerator[s]; If[PrimeQ[k], Print[n]], {n, 1, 1500}]
Position[Accumulate[1/Prime[Range[120]]], _?(PrimeQ[ Numerator[ #]]&)] //Flatten (* To generate terms greater than 120, increase the Range constant, but the program may take much longer to run. *) (* Harvey P. Dale, Jan 01 2019 *)
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CROSSREFS
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KEYWORD
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hard,more,nonn
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AUTHOR
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STATUS
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approved
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