A121660 Numerator of fraction equal to the continued fraction [4, 6, 9, ..., semiprime(n)].

4, 25, 229, 2315, 32639, 491900, 10362539, 228467758, 5722056489, 149001936472, 4922785960065, 167523724578682, 5868253146213935, 223161143280708212, 8709152841093834203, 400844191833597081550, 19650074552687350830153

Offset

1,1

Comments

Denominator of fraction equal to the continued fraction [4, 6, 9, ..., semiprime(n)] is A121661. Hence A121660/A121661 is semiprime analog of A036247/A036248.

Apparently the same as A118835. - Georg Fischer, Oct 03 2018

Links

Robert Israel, Table of n, a(n) for n = 1..376

Formula

Numerator of fraction equal to the continued fraction [4, 6, 9, ..., A001358(n)].

Example

a(1) = numerator of 4 = 4.
a(2) = numerator of 4 + 1/6 = numerator of 25/6 = 25.
a(3) = numerator of 4 + 1/(6+1/9)) = numerator of 229/55 = 229.
a(10) = numerator of 4+1/(6+1/(9+1/(10+ 1/(14+1/(15+ 1/(21+1/(22+1/(25+1/(26))))))))) = numerator of 149001936472/35786212191 = 149001936472.

Maple

SP:= select(t -> numtheory:-bigomega(t)=2, [$4..100]):
seq(numer(numtheory:-cfrac(SP[1..n])), n=1..nops(SP)); # Robert Israel, Jul 10 2018

Mathematica

Module[{nn=70, sps}, sps=Select[Range[nn], PrimeOmega[#]==2&]; Table[Numerator[ FromContinuedFraction[ Take[sps, n]]], {n, Length[sps]}]] (* Harvey P. Dale, Jan 09 2024 *)

Crossrefs

Cf. A001358, A036247, A036248, A121661.

Sequence in context: A031152 A010845 A087660 * A118835 A365053 A224080

Adjacent sequences: A121657 A121658 A121659 * A121661 A121662 A121663

Keyword

easy,frac,nonn

Author

Jonathan Vos Post, Aug 14 2006

Extensions

More terms from Arkadiusz Wesolowski, Jul 03 2011

Status

approved