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A107899
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Numbers k such that the sum of the terms of the continued fraction for prime(k)/k is prime.
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5
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1, 2, 4, 5, 7, 8, 13, 14, 16, 17, 20, 22, 23, 24, 31, 32, 37, 41, 44, 47, 49, 50, 63, 68, 69, 71, 73, 78, 81, 82, 84, 86, 89, 93, 98, 101, 109, 111, 119, 121, 126, 130, 131, 132, 135, 138, 142, 143, 145, 150, 164, 169, 175, 176, 189, 190, 197, 201, 202, 205, 211, 214
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OFFSET
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1,2
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COMMENTS
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Indices of primes occurring in A107900.
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LINKS
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EXAMPLE
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17 is in this sequence because the 17th prime is 59, 59/17 = 3 + 1/(2 + 1/8), the terms of the continued fraction are {3, 2, 8), and the sum of the terms is the prime number 13.
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MAPLE
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filter:= n -> isprime(convert(Term(NumberTheory:-ContinuedFraction(ithprime(n)/n), all), `+`)):
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MATHEMATICA
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s={}; Do[If[PrimeQ[Plus@@ContinuedFraction[Prime[n]/n]], s=Append[s, n]], {n, 300}]; A107899=s
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CROSSREFS
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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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