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 A271470 #47 Nov 30 2016 05:32:35 %S A271470 1,2241,18395521,22005481,180674890281,1483422094617961, %T A271470 1774530705782041,14569695060825930201,119623748111985974353561, %U A271470 143098862377484625247441,1174906008443637039413730321,9646506658002296058866816899921,11539549215467584644303744700081 %N A271470 a(n)-th chiliagonal (or 1000-gonal) number is square. %C A271470 a(n) is odd since a(n) mod 10 = A000012(n). Since all odd numbers with one or two distinct prime factors are deficient, a(n) is deficient. E.g., 18399811 = sigma(a(3)) < 2*a(3) = 36791042. - _Muniru A Asiru_, Nov 17 2016 %C A271470 The digital root of a(n) is always 1, 4, 7 or 9. - _Muniru A Asiru_, Nov 29 2016 %H A271470 Colin Barker, <a href="/A271470/b271470.txt">Table of n, a(n) for n = 1..380</a> %H A271470 M. A. Asiru, <a href="http://dx.doi.org/10.1080/0020739X.2016.1164346">All square chiliagonal numbers</a>, Int J Math Educ Sci Technol, 47:7(2016), 1123-1134. %H A271470 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,80640398,-80640398,0,-1,1). %F A271470 a(n)*(499*a(n)-498) = (A271115(n))^2 = A271105(n). %F A271470 a(n) = 80640398*a(n-3) - a(n-6) - 40239396, for n>6. %F A271470 a(n) = 40320199*a(n-3) + 1804980*A271115(n-3) - 20119698, for n>3. - _Muniru A Asiru_, Apr 09 2016 %F A271470 G.f.: x*(1+2240*x+18393280*x^2-77030438*x^3+18393280*x^4+2240*x^5+x^6) / ((1-x)*(1-80640398*x^3+x^6)). - _Colin Barker_, Apr 09 2016 %e A271470 a(2)=2241. %e A271470 The 2241st chiliagonal number is a square because 2241*(499*2241 - 498) = 2504902401 = (A271115(2))^2 = A271105(2); %e A271470 the 22005481st chiliagonal number is a square because 22005481*(499*22005481 - 498) = (A271115(4))^2 = A271105(4). %o A271470 (GAP) %o A271470 g:=1000; %o A271470 S:=[2*[ 500, 1 ], 4*[ 1022201, 22880 ], 498*[ 8980, 201 ], 996*[ 1, 0 ],-2*[- 500, 1 ], -4*[- 1022201, 22880 ]];; Length(S); %o A271470 u:=40320199;; v:=902490;; G:=[[u,2*(g-2)*v],[v,u]];; %o A271470 A:=List([1..Length(S)],s->List(List([0..6],i->G^i*TransposedMat([S[s]])),Concatenation));; Length(A); %o A271470 D1:=Union(List([1..Length(A)],k->A[k]));; Length(D1); %o A271470 D2:=List(D1,i-> [(i[1]+(g-4))/(2*(g-2)),i[2]/2] );; %o A271470 D3:=Filtered(D2,i->IsInt(i[1])); %o A271470 D4:=Filtered(D3,i->i[2]>0); %o A271470 D5:=List(D4,i->i[1]); # chiliagonal (or 1000-gonal) number is square %o A271470 (PARI) Vec(x*(1+2240*x+18393280*x^2-77030438*x^3+18393280*x^4+2240*x^5+x^6)/((1-x)*(1-80640398*x^3+x^6)) + O(x^50)) \\ _Colin Barker_, Apr 09 2016 %Y A271470 Cf. A271115, A271105. %K A271470 nonn,easy %O A271470 1,2 %A A271470 _Muniru A Asiru_, Apr 08 2016 %E A271470 More terms from _Colin Barker_, Apr 09 2016