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 A161588 #5 Jun 14 2016 13:23:25 %S A161588 0,13,2184,364728,60907405,10171171920,1698524803248,283643470970509, %T A161588 47366761127271768,7909965464783414760,1320916865857702993165, %U A161588 220585206632771616443808,36836408590807002243122784,6151459649458136602985061133,1027256925050918005696262086440 %N A161588 The list of the k values in the common solutions to the 2 equations 11*k+1=A^2, 15*k+1=B^2. %C A161588 The 2 equations are equivalent to the Pell equation x^2-165*y^2=1, %C A161588 with x=(165*k+13)/2 and y=A*B/2, case C=11 in A160682. %H A161588 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (168,-168,1). %F A161588 k(t+3)=168*(k(t+2)-k(t+1))+k(t). %F A161588 k(t)=((13+w)*((167+13*w)/2)^(t-1)+(13-w)*((167-13*w)/2)^(t-1))/330 where w=sqrt(165). %F A161588 k(t) = floor of ((13+w)*((167+13*w)/2)^(t-1))/330; %F A161588 G.f.: -13*x^2/((x-1)*(x^2-167*x+1)). %p A161588 t:=0: for n from 0 to 1000000 do a:=sqrt(11*n+1): b:=sqrt(15*n+1): %p A161588 if (trunc(a)=a) and (trunc(b)=b) then t:=t+1: print(t,n,a,b): end if: end do: %Y A161588 Cf. A160682, A085260 (sequence of A), A126816 (sequence of B). %K A161588 nonn,easy %O A161588 1,2 %A A161588 _Paul Weisenhorn_, Jun 14 2009 %E A161588 Edited, extended by _R. J. Mathar_, Sep 02 2009