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A242382
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Lesser of consecutive primes whose average is a perfect cube.
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2
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61, 1723, 4093, 17573, 21943, 46649, 110587, 195103, 287491, 314423, 405221, 474547, 1061189, 1191013, 1404919, 1601609, 1906621, 2000371, 2146687, 2196979, 3241783, 3511799, 4912991, 5268017, 6229501, 6751267, 6858997, 7077883, 11239421, 20346407, 21951997, 26198063
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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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1723 is in the sequence because it is prime, nextprime(1723) = 1733, and average(1723,1733) = 1728 = 12^3.
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MATHEMATICA
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Select[Partition[Prime[Range[2, 10^5]], 2, 1], IntegerQ[Surd[(First[#] + Last[#])/2, 3]] &][[;; , 1]] (* Amiram Eldar, Jul 04 2022 *)
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PROG
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(PARI) {for(i=3, 3*10^7, if(isprime(i), k=(i+nextprime(i+1))/2; if(ispower(k, 3), print1(i, ", "))))}
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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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