A240859 Cubes k^3 such that k^3 + (k+1)^3 is semiprime.
1, 8, 27, 125, 216, 512, 2744, 3375, 8000, 9261, 35937, 68921, 125000, 157464, 328509, 421875, 474552, 704969, 729000, 970299, 1157625, 1367631, 1685159, 2248091, 2628072, 2803221, 3581577, 3723875, 4741632, 5177717, 5451776, 6751269, 7301384, 9129329, 9938375
Offset: 1
Examples
a(2) = 8 = 2^3: 2^3 + 3^3 = 35 = 5*7 which is a semiprime. a(4) = 125 = 5^3: 5^3 + 6^3 = 341 = 11*31 which is a semiprime.
Links
- K. D. Bajpai, Table of n, a(n) for n = 1..3689
Programs
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Maple
with(numtheory):KD:= proc() local a,b; a:=n^3+(n+1)^3;b:=bigomega(a); if b=2 then RETURN (n^3); fi; end: seq(KD(), n=1..500);
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Mathematica
Transpose[Select[Partition[Range[250]^3,2,1],PrimeOmega[Total[#]] == 2&]] [[1]] (* Harvey P. Dale, Dec 15 2015 *)
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PARI
forprime(p=3,1e4,if(isprime((p^2+3)/4),print1((p^3 - 3*p^2 + 3*p - 1)/8", "))) \\ Charles R Greathouse IV, Aug 25 2014