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 A036247 #27 Aug 10 2025 10:33:14
%S A036247 2,7,37,266,2963,38785,662308,12622637,290982959,8451128448,
%T A036247 262275964847,9712661827787,398481410904114,17144413330704689,
%U A036247 806185907954024497,42744997534894003030,2522761040466700203267
%N A036247 Numerator of fraction equal to the continued fraction [ 2, 3, 5, ...prime(n) ].
%F A036247 a(1)=2; a(2)=7; for n>2, a(n)=prime(n)*a(n-1)+a(n-2). - _Zak Seidov_, Nov 07 2008
%e A036247 a(2)=7 because 2+1/3 = 7/3.
%e A036247 a(3)=37 because 2+1/(3+1/5) = 37/16.
%e A036247 a(4)=266 because 2+1/(3+1/(5+1/7)) = 266/115.
%t A036247 a[1]=2;a[2]=7;a[n_]:=Prime[n]*a[n-1]+a[n-2];Table[a[n],{n,20}] (* _Zak Seidov_, Nov 07 2008 *)
%t A036247 With[{prs=Prime[Range[20]]},Numerator[Table[FromContinuedFraction[ Take[ prs,n]],{n,20}]]] (* _Harvey P. Dale_, Dec 02 2011 *)
%o A036247 (PARI) a(n)=if(n<0,0,contfracpnqn(vector(n,i, prime(i)))[1,1])
%Y A036247 Cf. A036248 (denominator), A083659.
%K A036247 frac,nonn
%O A036247 1,1
%A A036247 _Jeff Burch_
%E A036247 More terms from _Benoit Cloitre_, May 25 2003