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A076661 Index of first term of the harmonic sequence having the same denominator as the partial harmonic sequence beginning with 1/n. 0
1, 2, 4, 9, 9, 10, 10, 14, 25, 27, 27, 27, 27, 27, 27, 27, 49, 49, 49, 49, 49, 49, 49, 49, 49, 50, 50, 125, 125, 125, 125, 125, 125, 125, 143, 143, 143, 143, 143, 136, 136, 136, 136, 136, 136, 136, 136, 136, 136, 136, 98, 98, 98, 133, 133, 133, 133, 125, 125, 125, 125 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Of more interest is the index of terms after which the denominators of the harmonic sequence always match the denominators of the partial harmonic sequence. Notice that 1/4+..1/21 has denominator 15519504, but 1/1+1/2+..1/21 has denominator 5173168.
LINKS
EXAMPLE
a(4) = firstHM[4] = 9 because 1/4+1/5+1/6+1/7+1/8+1/9 has the same denominator (2520) as 1/1+1/2+..+1/8+1/9 (and the sums to 4,5,6,7 and 8 do not).
MATHEMATICA
harmNumber[m_, n_] := HarmonicNumber[n] - HarmonicNumber[m - 1]; denH[n_] := Denominator[HarmonicNumber[n]]; denH[m_, n_] := Denominator[harmNumber[m, n]]; firstHM[m_] := Do[If[denH[k] == denH[m, k], Return[k], ], {k, m, 10^4}]
CROSSREFS
Cf. A002805.
Sequence in context: A244285 A111422 A279035 * A258710 A246515 A275658
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified July 14 22:52 EDT 2024. Contains 374323 sequences. (Running on oeis4.)