A118835 -id:A118835 - cp's OEIS frontend

A121660 Duplicate of A118835.

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

Offset: 1

Jonathan Vos Post, Aug 14 2006

dead

Previous name was: Numerator of fraction equal to the continued fraction [4, 6, 9, ..., semiprime(n)].

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

			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.

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

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

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 *)

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

More terms from Arkadiusz Wesolowski, Jul 03 2011

A118836 Denominators of n-th convergent to continued fraction with semiprime terms.

Original entry on oeis.org

1, 6, 55, 556, 7839, 118141, 2488800, 54871741, 1374282325, 35786212191, 1182319284628, 40234641889543, 1409394785418633, 53597236487797597, 2091701617809524916, 96271871655725943733, 4719413412748380767833, 240786355921823145103216, 13247968989113021361444713

Offset: 1

Jonathan Vos Post, May 01 2006

Numerators are A118835. A118835/A118836 converges to semiprime continued fraction constant ~ 4.1636688.

These are to semiprimes as A001053 are to natural numbers. See also A105815 Decimal expansion of the semiprime nested radical.

			a(1) = 1 = denominator of 4/1.
a(2) = 6 = denominator of 25/6 = 4+1/6.
a(3) = 55 = denominator of 229/55 = 4+1/(6+1/9).
a(4) = 556 = denominator of 2315/556 = 4+1/(6+1/(9+(1/10))).
The first fractions are 4, 25/6, 229/55, 2315/556, 32639/7839, 491900/118141, 10362539/2488800, 228467758/54871741, 5722056489/1374282325, 149001936472/35786212191, 4922785960065/1182319284628, 167523724578682/40234641889543, 5868253146213935/1409394785418633.

Eric Weisstein's World of Mathematics, Continued Fraction Constant.

Cf. A001358, A001040, A001053, A105815, A118835.

sp = Select[Range[10^3], PrimeOmega[#] == 2 &]; Denominator @ Table[ FromContinuedFraction[ Take[sp, i]], {i, 20}] (* Giovanni Resta, Jun 16 2016 *)

a(n) = denominator of continued fraction [4; 6, 9, 10, 14, ... A001358(n)]. CONTINUANT transform of A001358.

Corrected and edited by Giovanni Resta, Jun 16 2016

cp's OEIS Frontend

A121660 Duplicate of A118835.

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