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A240339
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Primes p which are floor of Root-Mean-Cube (RMC) of prime(n) and prime(n+1).
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1
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59, 97, 1321, 1621, 2539, 3511, 4339, 4889, 5591, 6491, 6917, 9419, 10289, 11689, 16381, 18719, 19441, 23053, 23567, 28499, 41051, 47143, 64661, 65203, 67939, 71023, 82493, 89107, 94999, 98927, 106087, 114941, 117281, 120823, 135647, 139361, 144289, 154799
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OFFSET
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1,1
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LINKS
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EXAMPLE
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13 and 17 are consecutive primes: sqrt((13^3 + 17^3)/2) = 59.62382073: floor(59.62382073)= 59, which is prime and appears in the sequence.
19 and 23 are consecutive primes: sqrt((19^3 + 23^3)/2) = 97.53460923: floor(97.53460923)= 97, which is prime and appears in the sequence.
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MAPLE
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KD := proc() local a, b, d; a:=ithprime(n); b:=ithprime(n+1); d:=floor(evalf(sqrt(((a^3+b^3)/2)))); if isprime(d) then RETURN (d); fi; end: seq(KD(), n=1..1000);
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MATHEMATICA
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Select[Floor[Sqrt[Mean[#]]]&/@(Partition[Prime[Range[600]], 2, 1]^3), PrimeQ] (* Harvey P. Dale, Sep 24 2014 *)
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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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