cp's OEIS Frontend

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.

A349500 a(n) is the least number k such that A349474(k) = A349474(k+1) = n, or -1 if no such k exists.

Original entry on oeis.org

2, 7, 76, 56, 81, 63, 913, 892, 1969, 4824, 22855, 16819, 48922, 170649, 273216, 607783, 1204354, 1910608, 3433671, 10104969, 19546522, 21424744, 66961728, 103366113, 217458328, 813832568, 771821712, 2370545332, 4638470426, 7190276806, 9309810824, 35730615937
Offset: 2

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Author

Amiram Eldar, Nov 20 2021

Keywords

Comments

The sequence begins at n = 2. a(1) != -1 if and only if two consecutive harmonic numbers exist. There are no odd harmonic numbers between 2 and 10^24 (Cohen and Sorli, 2010) and it is conjectured that they do not exist.

Examples

			a(2) = 2 since A349474(2) = A349474(3) = 2 and there is no smaller pair of consecutive numbers with this property.
a(3) = 7 since A349474(7) = A349474(8) = 3 and there is no smaller pair of consecutive numbers with this property.
		

Crossrefs

Programs

  • Mathematica
    c[n_] := Length @ ContinuedFraction[DivisorSigma[0, n]/DivisorSigma[-1, n]]; seq[len_, nmax_] := Module[{s = Table[0, {len}], k = 1, n = 1, i}, s[[1]] = -1; While[n < nmax && k < len, i = c[n]; If[c[n+1] == i && i <= len && s[[i]] == 0, k++; s[[i]] = n]; n++]; Rest @ s]; seq[15, 10^6]