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.
11 does not qualify for the term after 10 because the sum of the reciprocals of the first 11 terms would then fall between 3.01 and 3.02.
a(3)=13 is the number of terms of A140335; a(4)=35 is the number of terms of A281873.
from sympy import egyptian_fraction def A306349(n): return len(egyptian_fraction((n,1)))
a(3) = 57960 because (1/1) + (1/2) + (1/3) + (1/4) + (1/5) + (1/6) + (1/7) + (1/8) + (1/9) + (1/10) + (1/15) + (1/230) + (1/57960) = 3 and the final and greatest denominator is 57960. (Sequence A140335 has the full list of denominators.)
a(n)={my(s=n,k=1); while(s>1/k, s-=1/k; k++); while(s!=0, k=ceil(1/s); s-=1/k); k} \\ Andrew Howroyd, Sep 01 2019
from sympy import egyptian_fraction def A323725(n): return egyptian_fraction((n,1))[-1] # Pontus von Brömssen, Aug 03 2020
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