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

1,2

Links

Table of n, a(n) for n=1..10.

Example

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.

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]

Crossrefs

Cf. A349474, A349499, A349500.

Sequence in context: A100273 A138982 A142666 * A283489 A051055 A003827

Adjacent sequences: A349498 A349499 A349500 * A349502 A349503 A349504

Keyword

nonn,more

Author

Amiram Eldar, Nov 20 2021

Status

approved