login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A207385 A206818(n+1)-A206818(n). 2
1, 2, 2, 2, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 3, 1, 2, 2, 1, 3, 2, 2, 1, 2, 3, 2, 2, 2, 2, 2, 1, 2, 2, 3, 2, 2, 1, 2, 3, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 3, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 3, 2, 1, 2, 2, 3, 1, 2, 2, 1, 2, 3, 2, 2, 2, 1, 2, 3, 2, 1, 2, 2, 3, 2, 2, 1, 2, 2, 3, 2, 2, 2, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The sequences A206815, A206818, A207384, A207835 illustrate the closeness of {j+pi(j)} to {k+(k+1)/log(k+1)}, as suggested by the prime number theorem and the conjecture that all the terms of A207384 and A207835 are in the set {1,2,3}.

LINKS

Table of n, a(n) for n=1..99.

EXAMPLE

The joint ranking is represented by

1 < 3 < 3.8 < 4.7 < 5 < 5.8 < 6 <7.1 < 8 < 8.3 < 9 < ...

Positions of numbers j+pi(j): 1,2,5,7,9,...

Positions of numbers k+(k+1)/log(k+1): 3,4,6,8,10,..

MATHEMATICA

f[1, n_] := n + PrimePi[n];

f[2, n_] := n + N[(n + 1)/Log[n + 1]]; z = 500;

t[k_] := Table[f[k, n], {n, 1, z}];

t = Sort[Union[t[1], t[2]]];

p[k_, n_] := Position[t, f[k, n]];

Flatten[Table[p[1, n], {n, 1, z}]]    (* A206815 *)

Flatten[Table[p[2, n], {n, 1, z}]]    (* A206818 *)

d1[n_] := p[1, n + 1] - p[1, n]

Flatten[Table[d1[n], {n, 1, z - 1}]]  (* A207385 *)

d2[n_] := p[2, n + 1] - p[2, n]

Flatten[Table[d2[n], {n, 1, z - 1}]]  (* A207386 *)

CROSSREFS

Cf. A000720, A206815, A206818.

Sequence in context: A306250 A145443 A192056 * A306242 A118144 A136691

Adjacent sequences:  A207382 A207383 A207384 * A207386 A207387 A207388

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 17 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 25 07:53 EDT 2019. Contains 324347 sequences. (Running on oeis4.)