OFFSET
1,1
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
LINKS
K. D. Bajpai, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)
FORMULA
a(1)=1+3t*(t+1) with t=5, a(2)=1+3t*(t+1) with t=7.
EXAMPLE
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.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Giacomo Fecondo, Apr 28 2009
STATUS
approved