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A094663
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Prime numerators of the sums of the ratios of consecutive primes.
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0
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OFFSET
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2,1
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COMMENTS
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Sum of reciprocals = 0.5577902661277818841795751911..
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LINKS
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FORMULA
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If a(n) = Sum(prime(k)/prime(k+1), k=1..n)) is prime.
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EXAMPLE
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2/3 + 3/5 +5/7 + 7/11 = 3023/1155. 3023 is prime, the third entry in the sequence.
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MATHEMATICA
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Select[Numerator/@Accumulate[First[#]/Last[#]&/@ Partition[Prime[ Range[50]], 2, 1]], PrimeQ] (* Harvey P. Dale, Apr 23 2011 *)
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PROG
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(PARI) consecpr2(n) = { s=0; y=0; forprime(x=2, n, y+=x/nextprime(x+1); z=numerator(y); s+=1./z; if(isprime(z), print1(z", ")) ); print(); print(s) }
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CROSSREFS
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KEYWORD
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frac,nonn
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AUTHOR
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EXTENSIONS
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The next term is too large to include.
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STATUS
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approved
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