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%I #19 Oct 24 2020 16:54:15
%S 2,7,37,266,2963,38785,662308,12622637,290982959,8451128448,
%T 262275964847,9712661827787,398481410904114,17144413330704689,
%U 806185907954024497,42744997534894003030,2522761040466700203267
%N Numerator of fraction equal to the continued fraction [ 2, 3, 5, ...prime(n) ].
%F a(1)=2; a(2)=7; for n>2, a(n)=prime(n)*a(n-1)+a(n-2) [From _Zak Seidov_, Nov 07 2008]
%e a(2)=7 because 2+1/3 = 7/3. a(3)=37 because 2+1/(3+1/5) = 37/16. a(4)=266 because 2+1/(3+1/(5+1/7)) = 266/115.
%t a[1]=2;a[2]=7;a[n_]:=Prime[n]*a[n-1]+a[n-2];Table[a[n],{n,20}] [From _Zak Seidov_, Nov 07 2008]
%t With[{prs=Prime[Range[20]]},Numerator[Table[FromContinuedFraction[ Take[ prs,n]],{n,20}]]] (* _Harvey P. Dale_, Dec 02 2011 *)
%o (PARI) a(n)=if(n<0,0,contfracpnqn(vector(n,i, prime(i)))[1,1])
%Y Cf. A036248, A083659.
%K frac,nonn
%O 1,1
%A _Jeff Burch_
%E More terms from _Benoit Cloitre_, May 25 2003
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