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 A243813 #24 Mar 17 2024 07:43:43 %S A243813 1,1,1,1,1,3,1,1,1,5,1,1,1,2,9,1,1,1,1,3,13,1,1,1,1,2,5,19,1,1,1,1,1, %T A243813 3,7,25,1,1,1,1,1,2,4,9,33,1,1,1,1,1,1,2,5,11,41,1,1,1,1,1,1,2,3,6,14, %U A243813 51,1,1,1,1,1,1,1,2,4,7,17,61,1,1,1,1,1,1,1,2,3,5,9,21 %N A243813 Table read by antidiagonals: T(n,k) is the curvature (truncated to integer) of a circle in a variation of nested Pappus chains (see Comments for details). %C A243813 Refer to the construction rule used in A243618. For this case, the curvature is defined by (-1/k, 1/(k-1), 1), the circle radius will diverge to infinity (zero curvature). The integral curvatures appearing as periodic, i.e., 2, 6, 6, 10, 30, 42, 28, 12, ..., = A083482(k-1). The integral curvatures seem to align as some sequence, e.g., 3, 7, 13, 21, 31, 43, ..., = A002061(k) and 9, 25, 49, ..., = A016754(k-1). See illustration. %H A243813 Kival Ngaokrajang, <a href="/A243813/a243813.pdf">Illustration for k = 2..7</a> %e A243813 Table begins: %e A243813 n/k 2 3 4 5 6 7 ... %e A243813 0 1 1 1 1 1 1 ... %e A243813 1 1 1 1 1 1 1 ... %e A243813 2 3 1 1 1 1 1 ... %e A243813 3 5 2 1 1 1 1 ... %e A243813 4 9 3 2 1 1 1 ... %e A243813 5 13 5 3 2 1 1 ... %e A243813 6 19 7 4 2 2 1 ... %e A243813 7 25 9 5 3 2 2 ... %e A243813 8 33 11 6 4 3 2 ... %e A243813 9 41 14 7 5 3 2 ... %e A243813 10 51 17 9 6 4 3 ... %e A243813 11 61 21 11 7 5 3 ... %e A243813 12 73 25 13 8 5 4 ... %e A243813 ... %o A243813 (Small Basic) %o A243813 For k=2 to 100 %o A243813 a=-k %o A243813 b=k-1 %o A243813 c=1 %o A243813 aa[0][k]=1 %o A243813 For n = 1 To 100 %o A243813 x=a*b*c %o A243813 y=Math.Power(x*(a+b+c),1/2) %o A243813 r=x/(a*b+a*c+b*c-2*y) %o A243813 aa[n][k]= math.floor(1/r) %o A243813 If 1/r-math.Floor(1/r)> 0.999999 Then %o A243813 aa[n][k]=aa[n][k]+1 %o A243813 EndIf %o A243813 c=r %o A243813 EndFor %o A243813 endFor %o A243813 '===================================== %o A243813 For t = 1 to 30 %o A243813 d=0 %o A243813 For nn=0 To t-1 %o A243813 kk=t+1-d %o A243813 TextWindow.Write(aa[nn][kk]+", ") %o A243813 d=d+1 %o A243813 EndFor %o A243813 Endfor %Y A243813 Cf. A243618, A083482, A002061, A016754. %Y A243813 Cf. Column 1 = A080827(n), column 2 = A056827(n) + 1. %Y A243813 Cf. Integral curvature in column 1..6: [A058331, A227776, A056107, A212656, A158558, A158604]. %K A243813 nonn,tabl %O A243813 0,6 %A A243813 _Kival Ngaokrajang_, Jun 11 2014