A364872 Lexicographically earliest continued fraction which is its own unit fraction series.
2, 1, 2, 2, 5, 95, 137447, 19092121105, 1456654254113777258001, 8728918703159963392919895262580124849062181
Offset: 0
Examples
The partial continued fraction must always be strictly larger than the partial unit fractions: [1] cannot be since 1 = 1. [2] can be since 2 > 1/2. [2,1] can be since 2+1/1 > 1/2+1/1. [2,1,1] cannot be since 2+1/(1+1/1) = 1/2+1/1+1/1. [2,1,2] can be since 2+1/(1+1/2) > 1/2+1/1+1/2. ... sum(1/a[n]) = 2.71053359137351078733864566... (A364873).
Crossrefs
Cf. A364873.
Programs
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PARI
cf(a) = my(m=contfracpnqn(a)); m[1,1]/m[2,1]; uf(a) = sum(i=1, #a, 1/a[i]); 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};
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