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A120398
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Sums of two distinct prime cubes.
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18
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35, 133, 152, 351, 370, 468, 1339, 1358, 1456, 1674, 2205, 2224, 2322, 2540, 3528, 4921, 4940, 5038, 5256, 6244, 6867, 6886, 6984, 7110, 7202, 8190, 9056, 11772, 12175, 12194, 12292, 12510, 13498, 14364, 17080, 19026, 24397, 24416, 24514
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OFFSET
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1,1
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COMMENTS
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If an element of this sequence is odd, it must be of the form a(n)=8+p^3, else it is a(n)=p^3+q^3 with two primes p>q>2. - M. F. Hasler, Apr 13 2008
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LINKS
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FORMULA
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EXAMPLE
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2^3+3^3=35=a(1), 2^3+5^3=133=a(2), 3^3+5^3=152=a(3), 2^3+7^3=351=a(4).
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MATHEMATICA
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Select[Sort[ Flatten[Table[Prime[n]^3 + Prime[k]^3, {n, 15}, {k, n - 1}]]], # <= Prime[15^3] &]
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PROG
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(PARI) isA030078(n)=n==round(sqrtn(n, 3))^3 && isprime(round(sqrtn(n, 3))) \\ M. F. Hasler, Apr 13 2008
(PARI) isA120398(n)={ n%2 & return(isA030078(n-8)); n<35 & return; forprime( p=ceil( sqrtn( n\2+1, 3)), sqrtn(n-26.5, 3), isA030078(n-p^3) & return(1))} \\ M. F. Hasler, Apr 13 2008
(PARI) for( n=1, 10^6, isA120398(n) & print1(n", ")) \\ - M. F. Hasler, Apr 13 2008
(PARI) list(lim)=my(v=List()); lim\=1; forprime(q=3, sqrtnint(lim-8, 3), my(q3=q^3); forprime(p=2, min(sqrtnint(lim-q3, 3), q-1), listput(v, p^3+q3))); Set(v) \\ Charles R Greathouse IV, Mar 31 2022
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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