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

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

Offset

1,2

Comments

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

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

Links

Table of n, a(n) for n=1..18.

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

Formula

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

Example

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))).

Mathematica

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

Crossrefs

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

Sequence in context: A215853 A110431 A121661 * A079589 A371776 A372210

Adjacent sequences: A118833 A118834 A118835 * A118837 A118838 A118839

Keyword

easy,frac,nonn

Author

Jonathan Vos Post, May 01 2006

Extensions

Corrected and edited by Giovanni Resta, Jun 16 2016

Status

approved