A206928 -id:A206928 - cp's OEIS frontend

A206929 Position of n+sin(n) when {k+cos(k)} and {k+sin(k)} are jointly ranked; complement of A206928.

3, 5, 6, 7, 9, 11, 13, 17, 19, 20, 21, 23, 25, 29, 31, 32, 33, 35, 37, 41, 43, 44, 45, 47, 49, 53, 55, 57, 58, 59, 61, 63, 67, 69, 70, 71, 73, 75, 79, 81, 82, 83, 85, 87, 91, 93, 94, 95, 97, 99, 101, 105, 107, 108, 109, 111, 113, 117, 119, 120, 121, 123, 125

Offset: 1

Clark Kimberling, Feb 13 2012

nonn

Cf. A206928.

f[n_] := N[n + Cos[n]]; z = 120;
g[n_] := N[n + Sin[n]];
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}]]    (* A206928 *)
Flatten[Table[q[n], {n, 1, z}]]    (* A206929 *)

A206911 Position of n-th partial sum of the harmonic series when all the partial sums are jointly ranked with the set {log(k+1)}; complement of A206912.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Feb 13 2012

nonn

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.

Similar conjectures can be stated for difference sequences based on jointly ranked sets, such as A206903, A206906, A206928, A206805, A206812, and A206815.

			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
A206911=(2,5,8,...).

Cf. A206912, A206815.

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 *)

cp's OEIS Frontend

A206929 Position of n+sin(n) when {k+cos(k)} and {k+sin(k)} are jointly ranked; complement of A206928.

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