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A036247
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Numerator of fraction equal to the continued fraction [ 2, 3, 5, ...prime(n) ].
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4
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2, 7, 37, 266, 2963, 38785, 662308, 12622637, 290982959, 8451128448, 262275964847, 9712661827787, 398481410904114, 17144413330704689, 806185907954024497, 42744997534894003030, 2522761040466700203267
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| a(1)=2; a(2)=7; for n>2: a (n)=prime(n)*a(n-1)+a(n-2) [From Zak Seidov (zakseidov(AT)yahoo.com), Nov 07 2008]
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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.
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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 (zakseidov(AT)yahoo.com), Nov 07 2008]
With[{prs=Prime[Range[20]]}, Numerator[Table[FromContinuedFraction[ Take[ prs, n]], {n, 20}]]] (* From Harvey P. Dale, Dec 02 2011 *)
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PROG
| (PARI) a(n)=if(n<0, 0, contfracpnqn(vector(n, i, prime(i)))[1, 1])
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CROSSREFS
| Cf. A036248, A083659.
Sequence in context: A001515 A144301 A083659 * A107877 A001028 A116481
Adjacent sequences: A036244 A036245 A036246 * A036248 A036249 A036250
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KEYWORD
| frac,nonn
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AUTHOR
| Jeff Burch (gburch(AT)erols.com)
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EXTENSIONS
| More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), May 25 2003
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