A036248 Denominator of fraction equal to the continued fraction [ 2, 3, 5, ..., prime(n) ].

1, 3, 16, 115, 1281, 16768, 286337, 5457171, 125801270, 3653694001, 113390315301, 4199095360138, 172276300080959, 7412079998841375, 348540036245625584, 18480034001016997327, 1090670546096248467877, 66549383345872173537824, 4459899354719531875502085

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..350

Formula

a(1) = 1, a(2) = 3, a(n) = A000040(n) * a(n-1) + a(n-2). - Daniel Suteu, Dec 20 2016

Example

Prime(4) = 7, and 2+1/(3+1/(5+1/7)) = 266/115, so a(4) = 115. - Jon E. Schoenfield, Dec 20 2016

Mathematica

With[{nn=20}, {prs=Prime[Range[nn]]}, Table[FromContinuedFraction[Take[prs, n]], {n, nn}]]//Denominator (* Harvey P. Dale, Sep 27 2025 *)

Prog

(PARI) a(n)=if(n<0, 0, contfracpnqn(vector(n, i, prime(i)))[2, 1])

Crossrefs

Cf. A000040, A036247.

Sequence in context: A177402 A036244 A011818 * A111555 A336293 A355718

Adjacent sequences: A036245 A036246 A036247 * A036249 A036250 A036251

Keyword

frac,easy,nonn

Author

Jeff Burch

Extensions

More terms from Benoit Cloitre, May 25 2003

Status

approved