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A349500
a(n) is the least number k such that A349474(k) = A349474(k+1) = n, or -1 if no such k exists.
1
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
2,1
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.
LINKS
Graeme L. Cohen and Ronald M. Sorli, Odd harmonic numbers exceed 10^24, Mathematics of Computation, Vol. 79, No. 272 (2010), pp. 2451-2460.
EXAMPLE
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.
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]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 20 2021
STATUS
approved