

A226896


Position of log n in the joint ranking of harmonic numbers H(k) and {log k}, for k >= 1; complement of A226894.


3



1, 2, 4, 5, 7, 8, 10, 11, 13, 15, 16, 18, 19, 21, 22, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 40, 41, 43, 44, 46, 47, 49, 51, 52, 54, 55, 57, 58, 60, 61, 63, 65, 66, 68, 69, 71, 72, 74, 76, 77, 79, 80, 82, 83, 85, 86, 88, 90, 91, 93, 94, 96, 97, 99, 100, 102
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OFFSET

1,2


COMMENTS

If, in the definition, log k is replaced by g + log k, where g is the EulerMascheroni constant, then the position of log n is 2n1, which leads to a conjecture: limit[1/(H(n)  g  log n)  2n] = 1/3.


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000


EXAMPLE

log 1 < log 2 < H(1) < log 3 < log 4 < H(2) < ...


MATHEMATICA

z = 300; h[n_] := N[HarmonicNumber[n], 100]; t1 = Table[h[n], {n, 1, z}]; t2 = Table[N[Log[n], 100], {n, 1, 3 z}]; t3 = Union[t1, t2]; p[n_] := Position[t3, h[n]]; Flatten[Table[p[n], {n, 1, 3 z}]] (* A226894 *)
Differences[%] (* A226895 *)
Complement[Range[z], %%] (* A226896 *)


CROSSREFS

Cf. A001008(n)/A002805(n) (H(n)), A226894.
Sequence in context: A213219 A161750 A249400 * A175302 A288521 A067940
Adjacent sequences: A226893 A226894 A226895 * A226897 A226898 A226899


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Jun 21 2013


STATUS

approved



