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 A364872 #17 Aug 13 2023 03:33:30
%S A364872 2,1,2,2,5,95,137447,19092121105,1456654254113777258001,
%T A364872 8728918703159963392919895262580124849062181
%N A364872 Lexicographically earliest continued fraction which is its own unit fraction series.
%C A364872 Earliest infinite sequence {a0,a1,a2,a3,...} such that: a0+1/(a1+1/(a2+1/(a3+...))) = 1/a0 + 1/a1 + 1/a2 + 1/a3 + ...
%C A364872 There are infinitely many real numbers whose continued fraction is also their unit fraction series - they are dense on the interval (2,oo).
%e A364872 The partial continued fraction must always be strictly larger than the partial unit fractions:
%e A364872 [1] cannot be since 1 = 1.
%e A364872 [2] can be since 2 > 1/2.
%e A364872 [2,1] can be since 2+1/1 > 1/2+1/1.
%e A364872 [2,1,1] cannot be since 2+1/(1+1/1) = 1/2+1/1+1/1.
%e A364872 [2,1,2] can be since 2+1/(1+1/2) > 1/2+1/1+1/2.
%e A364872 ...
%e A364872 sum(1/a[n]) = 2.71053359137351078733864566... (A364873).
%o A364872 (PARI)
%o A364872 cf(a) = my(m=contfracpnqn(a)); m[1,1]/m[2,1];
%o A364872 uf(a) = sum(i=1, #a, 1/a[i]);
%o A364872 A364872(N) = {a=[2]; for(i=2, N, a=concat(a, if(cf(a)==uf(a), a[i-1], ceil(1/(cf(a)-uf(a))))); while(cf(a)<=uf(a), a[i]++)); a};
%Y A364872 Cf. A364873.
%K A364872 nonn,cofr
%O A364872 0,1
%A A364872 _Rok Cestnik_, Aug 11 2023