This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A118835 #11 Feb 16 2025 08:33:01
%S A118835 4,25,229,2315,32639,491900,10362539,228467758,5722056489,
%T A118835 149001936472,4922785960065,167523724578682,5868253146213935,
%U A118835 223161143280708212,8709152841093834203,400844191833597081550,19650074552687350830153,1002554646378888489419353,55160155625391554268894568
%N A118835 Numerators of n-th convergent to continued fraction with semiprime terms.
%C A118835 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.
%C A118835 These are to semiprimes as A001040 are to natural numbers. See also A105815 Decimal expansion of the semiprime nested radical.
%H A118835 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ContinuedFractionConstant.html">Continued Fraction Constant.</a>
%F A118835 a(n) = numerator of continued fraction [4; 6, 9, 10, 14, ... A001358(n)]. CONTINUANT transform of A001358.
%e A118835 a(1) = 4 = numerator of 4/1.
%e A118835 a(2) = 25 = numerator of 25/6 = 4+1/6.
%e A118835 a(3) = 229 = numerator of 229/55 = 4+1/(6+1/9).
%e A118835 a(4) = 2315 = numerator of 2315/556 = 4+1/(6+1/(9+(1/10))).
%t A118835 sp = Select[Range[10^3], PrimeOmega[#] == 2 &]; Numerator@ Table[ FromContinuedFraction[ Take[sp, i]], {i, 20}] (* _Giovanni Resta_, Jun 16 2016 *)
%Y A118835 Cf. A001358, A001040, A001053, A105815, A118836.
%K A118835 easy,frac,nonn
%O A118835 1,1
%A A118835 _Jonathan Vos Post_, May 01 2006
%E A118835 Data corrected by _Giovanni Resta_, Jun 16 2016