

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
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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



KEYWORD

nonn


AUTHOR



STATUS

approved



