

A159961


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


1



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
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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

T. D. Noe and 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

Cf. A003215, A002407, A221717.
Sequence in context: A051347 A293647 A225908 * A113530 A119148 A166059
Adjacent sequences: A159958 A159959 A159960 * A159962 A159963 A159964


KEYWORD

nonn


AUTHOR

Giacomo Fecondo, Apr 28 2009


STATUS

approved



