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

1,1

Links

Table of n, a(n) for n=1..17.

Formula

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]

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A036248, A083659.

Sequence in context: A135920 A001515 A144301 * A083659 A107877 A001028

Adjacent sequences: A036244 A036245 A036246 * A036248 A036249 A036250

Keyword

frac,nonn

Author

Jeff Burch

Extensions

More terms from Benoit Cloitre, May 25 2003

Status

approved