A036247 Numerator of fraction equal to the continued fraction [ 2, 3, 5, ...prime(n) ].

2, 7, 37, 266, 2963, 38785, 662308, 12622637, 290982959, 8451128448, 262275964847, 9712661827787, 398481410904114, 17144413330704689, 806185907954024497, 42744997534894003030, 2522761040466700203267

Offset: 1

Author

Jeff Burch

Keywords

• frac
• nonn

Examples

			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.
		

Crossrefs

Cf. A036248 (denominator), A083659.

Programs

Mathematica

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 *)
With[{prs=Prime[Range[20]]},Numerator[Table[FromContinuedFraction[ Take[ prs,n]],{n,20}]]] (* Harvey P. Dale, Dec 02 2011 *)

PARI

a(n)=if(n<0,0,contfracpnqn(vector(n,i, prime(i)))[1,1])

Formula

a(1)=2; a(2)=7; for n>2, a(n)=prime(n)*a(n-1)+a(n-2). - Zak Seidov, Nov 07 2008

Extensions

More terms from Benoit Cloitre, May 25 2003