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A036247 Numerator of fraction equal to the continued fraction [ 2, 3, 5, ...prime(n) ]. 5
2, 7, 37, 266, 2963, 38785, 662308, 12622637, 290982959, 8451128448, 262275964847, 9712661827787, 398481410904114, 17144413330704689, 806185907954024497, 42744997534894003030, 2522761040466700203267 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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
Sequence in context: A135920 A001515 A144301 * A083659 A107877 A001028
KEYWORD
frac,nonn
AUTHOR
EXTENSIONS
More terms from Benoit Cloitre, May 25 2003
STATUS
approved

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Last modified November 29 13:49 EST 2023. Contains 367445 sequences. (Running on oeis4.)