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A160830
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Integer part of the product of two consecutive primes divided by their sum.
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2
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1, 1, 2, 4, 5, 7, 8, 10, 12, 14, 16, 19, 20, 22, 24, 27, 29, 31, 34, 35, 37, 40, 42, 46, 49, 50, 52, 53, 55, 59, 64, 66, 68, 71, 74, 76, 79, 82, 84, 87, 89, 92, 95, 97, 98, 102, 108, 112, 113, 115, 117, 119, 122, 126, 129, 132, 134, 136, 139, 140, 143, 149, 154, 155, 157
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OFFSET
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1,3
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COMMENTS
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The differences a(n+1) - a(n) appear to grow without bound while the difference 2 appears to occur infinitely often.
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LINKS
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FORMULA
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a(n) = floor(prime(n)*prime(n+1)/(prime(n)+prime(n+1))) where prime(.)=A000040(.).
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EXAMPLE
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a(5) = floor(prime(5)*prime(6)/(prime(5)+prime(6))) = 5.
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MATHEMATICA
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Table[Floor[Prime[n]*Prime[n+1]/(Prime[n] +Prime[n+1])], {n, 1, 100}] (* G. C. Greubel, Apr 30 2018 *)
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PROG
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(PARI) g(x) = p1=prime(x); p2=prime(x+1); y=p1*p2/(p1+p2); floor(y);
g1(n) = for(j=1, n, print1(g(j)", "))
(Magma) [Floor(NthPrime(n)*NthPrime(n+1)/(NthPrime(n)+NthPrime(n+1))): n in [1..100]]; // G. C. Greubel, Apr 30 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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