

A206911


Position of nth partial sum of the harmonic series when all the partial sums are jointly ranked with the set {log(k+1)}; complement of A206912.


7



2, 5, 8, 11, 13, 16, 19, 22, 24, 27, 30, 33, 36, 38, 41, 44, 47, 49, 52, 55, 58, 61, 63, 66, 69, 72, 74, 77, 80, 83, 86, 88, 91, 94, 97, 100, 102, 105, 108, 111, 113, 116, 119, 122, 125, 127, 130, 133, 136, 138, 141, 142, 143, 144, 145, 146, 147, 148, 149
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OFFSET

1,1


COMMENTS

Conjecture: the difference sequence of A206911 consists of 2s and 3s, and the ratio (number of 3s)/(number of 2s) tends to a number between 3.5 and 3.6.


LINKS



EXAMPLE

Let S(n)=1+1/2+1/3+...+1/n and L(n)=log(n+1). Then
L(1)<S(1)<L(2)<L(3)<S(2)<L(4)<L(5)<S(3)<L(6)<..., so that


MATHEMATICA

f[n_] := Sum[1/k, {k, 1, n}]; z = 300;
g[n_] := N[Log[n + 1]];
c = Table[f[n], {n, 1, z}];
s = Table[g[n], {n, 1, z}];
j = Sort[Union[c, s]];
p[n_] := Position[j, f[n]]; q[n_] := Position[j, g[n]];
Flatten[Table[p[n], {n, 1, z}]] (* A206911 *)
Flatten[Table[q[n], {n, 1, z}]] (* A206912 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



