This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A084380 #43 Aug 27 2025 09:40:31
%S A084380 2,3,10,29,66,127,218,345,514,731,1002,1333,1730,2199,2746,3377,4098,
%T A084380 4915,5834,6861,8002,9263,10650,12169,13826,15627,17578,19685,21954,
%U A084380 24391,27002,29793,32770,35939,39306,42877,46658,50655,54874,59321,64002
%N A084380 a(n) = n^3 + 2.
%C A084380 This sequence contains no square numbers. A proof may be similar to the Hilliard link.
%H A084380 Vincenzo Librandi, <a href="/A084380/b084380.txt">Table of n, a(n) for n = 0..1000</a>
%H A084380 Dorin Andrica and Ovidiu Bagdasar, <a href="https://doi.org/10.1007/s11139-021-00418-7">On k-partitions of multisets with equal sums</a>, The Ramanujan J. (2021) Vol. 55, 421-435.
%H A084380 D. R. Heath-Brown, <a href="https://web.archive.org/web/20171121182817/http://eprints.maths.ox.ac.uk/165/1/x3%2B2.pdf">The largest prime factor of X^3 + 2</a>, Proc. London Math. Soc. (3), 82:3 (2001), pp. 554-596.
%H A084380 Cino Hilliard, <a href="https://web.archive.org/web/20080621104333/http://groups.msn.com:80/BC2LCC/n37ltk2.msnw">Proof that a cube plus 7 cannot be a square</a>
%H A084380 A. J. Irving, <a href="http://arxiv.org/abs/1412.0024">The largest prime factor of X^3+2</a>, arXiv:1412.0024 [math.NT], 2014.
%H A084380 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A084380 G.f.: (2 - 5*x + 10*x^2 - x^3) / (x-1)^4 . - _R. J. Mathar_, Feb 16 2011
%F A084380 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _Vincenzo Librandi_, Jun 24 2012
%t A084380 f[n_]:=n^3+2;f[Range[60]] (* Offset 1. *) (* _Vladimir Joseph Stephan Orlovsky_, Feb 14 2011 *)
%t A084380 CoefficientList[Series[(2-5*x+10*x^2-x^3)/(x-1)^4,{x,0,50}],x] (* _Vincenzo Librandi_, Jun 24 2012 *)
%o A084380 (PARI) n3pm(n,m=2) = { for(x=0,n,y=x^3+m; print1(y,", ")) }
%o A084380 (Magma) I:=[2, 3, 10, 29]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3) -Self(n-4): n in [1..50]]; // _Vincenzo Librandi_, Jun 24 2012
%Y A084380 Cf. sequences for n^3+7, n^3+17, n^3+3.
%Y A084380 Essentially the same as A034324.
%K A084380 easy,nonn,changed
%O A084380 0,1
%A A084380 _Cino Hilliard_, Jun 23 2003
%E A084380 Extended to offset 0 by _R. J. Mathar_, Feb 16 2011