A349501 a(n) is the least start of a run of exactly n consecutive numbers with the same length of the continued fraction of the harmonic mean of their divisors (A349474).
1, 2, 59, 280, 3539, 57575, 65, 15410548, 9286977451, 24510585369
Offset: 1
Examples
a(2) = 2 since A349474(2) = A349474(3) = 2 and there is no smaller pair of consecutive numbers with this property. a(3) = 59 since A349474(59) = A349474(60) = A349474(61) = 3 and there is no smaller triple of consecutive numbers with this property.
Programs
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Mathematica
d[n_] := Length @ ContinuedFraction[DivisorSigma[0, n] / DivisorSigma[-1, n]]; seq[len_, nmax_] := Module[{s = Table[0, {len}], dprev = -1, n = 1, c = 0, k = 0}, While[k < len && n < nmax, d1 = d[n]; If[d1 == dprev, c++, If[c > 0 && c <= len && s[[c]] == 0, k++; s[[c]] = n - c]; c = 1]; n++; dprev = d1]; TakeWhile[s, # > 0 &]]; seq[7, 10^5]