A159961 Cuban composites: composite numbers equal to the difference of two consecutive cubes.

91, 169, 217, 469, 721, 817, 1027, 1141, 1261, 1387, 1519, 2107, 2611, 2977, 3367, 3781, 3997, 4681, 4921, 5677, 5941, 6487, 6769, 7651, 7957, 8587, 8911, 9577, 9919, 10621, 10981, 11347, 12481, 12871, 14077, 14491, 14911, 15337, 15769, 16207, 17101, 17557

Offset: 1

Author

Giacomo Fecondo, Apr 28 2009

Keywords

• nonn

Comments

Analogous to the cuban primes A002407, but select the composite numbers rather than the primes.

Cuban composites are a subset of hexagonal centered numbers.

A cuban composite has an integer divisor of the form 6*k+1 other than 1 and itself.

Also, composite numbers of the form (n^2 + nm + m^2) where n and m are consecutive numbers. - K. D. Bajpai, Jun 12 2014

Examples

			a(1) = 91 = 1+3t*(t+1) with t = 5 is the smallest cuban composite number. Note that 91 = 7*13, so its factors have the form 6k+1, in fact 7 = 6*1+1.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Crossrefs

Cf. A003215, A002407, A221717.

Programs

Mathematica

nn = 200; Select[Table[3 x^2 + 3 x + 1, {x, nn}], ! PrimeQ[#] &] (* T. D. Noe, Jan 30 2013 *)
Select[Table[m=n+1;( n^2 + n m + m^2),{n,100}],!PrimeQ[#]&] (* K. D. Bajpai, Jun 12 2014 *)
Select[Differences[Range[80]^3],CompositeQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 07 2018 *)

Formula

a(1)=1+3t*(t+1) with t=5, a(2)=1+3t*(t+1) with t=7.