

A118836


Denominators of nth convergent to continued fraction with semiprime terms.


3



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



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



KEYWORD

easy,frac,nonn


AUTHOR



EXTENSIONS



STATUS

approved



