cp's OEIS Frontend

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

%I A159961 #20 Oct 30 2023 07:35:51
%S A159961 91,169,217,469,721,817,1027,1141,1261,1387,1519,2107,2611,2977,3367,
%T A159961 3781,3997,4681,4921,5677,5941,6487,6769,7651,7957,8587,8911,9577,
%U A159961 9919,10621,10981,11347,12481,12871,14077,14491,14911,15337,15769,16207,17101,17557
%N A159961 Cuban composites: composite numbers equal to the difference of two consecutive cubes.
%C A159961 Analogous to the cuban primes A002407, but select the composite numbers rather than the primes.
%C A159961 Cuban composites are a subset of hexagonal centered numbers.
%C A159961 A cuban composite has an integer divisor of the form 6*k+1 other than 1 and itself.
%C A159961 Also, composite numbers of the form (n^2 + nm + m^2) where n and m are consecutive numbers. - _K. D. Bajpai_, Jun 12 2014
%H A159961 K. D. Bajpai, <a href="/A159961/b159961.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)
%F A159961 a(1)=1+3t*(t+1) with t=5, a(2)=1+3t*(t+1) with t=7.
%e A159961 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.
%t A159961 nn = 200; Select[Table[3 x^2 + 3 x + 1, {x, nn}], ! PrimeQ[#] &] (* _T. D. Noe_, Jan 30 2013 *)
%t A159961 Select[Table[m=n+1;( n^2 + n m + m^2),{n,100}],!PrimeQ[#]&] (* _K. D. Bajpai_, Jun 12 2014 *)
%t A159961 Select[Differences[Range[80]^3],CompositeQ] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Apr 07 2018 *)
%Y A159961 Cf. A003215, A002407, A221717.
%K A159961 nonn
%O A159961 1,1
%A A159961 _Giacomo Fecondo_, Apr 28 2009