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A118835

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

4, 25, 229, 2315, 32639, 491900, 10362539, 228467758, 5722056489, 149001936472, 4922785960065, 167523724578682, 5868253146213935, 223161143280708212, 8709152841093834203, 400844191833597081550, 19650074552687350830153, 1002554646378888489419353, 55160155625391554268894568

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OFFSET

1,1

COMMENTS

Denominators are A118836. 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 A001040 are to natural numbers. See also A105815 Decimal expansion of the semiprime nested radical.

LINKS

Table of n, a(n) for n=1..19.

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

FORMULA

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

EXAMPLE

a(1) = 4 = numerator of 4/1.

a(2) = 25 = numerator of 25/6 = 4+1/6.

a(3) = 229 = numerator of 229/55 = 4+1/(6+1/9).

a(4) = 2315 = numerator of 2315/556 = 4+1/(6+1/(9+(1/10))).

MATHEMATICA