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

1,2

Links

K. D. Bajpai, Table of n, a(n) for n = 1..3689

Example

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.

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);

Mathematica

Transpose[Select[Partition[Range[250]^3, 2, 1], PrimeOmega[Total[#]] == 2&]] [[1]] (* Harvey P. Dale, Dec 15 2015 *)

Prog

(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

Crossrefs

Cf. A001358, A005898.

Sequence in context: A030162 A153147 A062838 * A277047 A046452 A030078

Adjacent sequences: A240856 A240857 A240858 * A240860 A240861 A240862

Keyword

nonn,easy

Author

K. D. Bajpai, Apr 13 2014

Status

approved