A073458 - OEIS

A073458

a(n) = floor(prime(n)/composite(n)).

0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 4, 4, 4, 4, 4

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OFFSET

1,16

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = floor(A000040(n)/A002808(n)).

MAPLE

nextcomp:= proc(x) if isprime(x+1) then x+2 else x+1 fi end proc:

p:= 2; c:= 4: A[1]:= 0:

for n from 2 to 200 do

p:= nextprime(p); c:= nextcomp(c);

A[n]:= floor(p/c);

od:

seq(A[i], i=1..200); # Robert Israel, Sep 28 2016

MATHEMATICA

Composite[n_] := FixedPoint[n + PrimePi[#] + 1&, n + PrimePi[n] + 1];

a[n_] := Floor[Prime[n]/Composite[n]];

Array[a, 100] (* Jean-François Alcover, Jun 09 2020, after Robert G. Wilson v in A002808 *)

Module[{nn=200, cmps}, cmps=Select[Range[nn], CompositeQ]; Floor[#[[1]]/ #[[2]]]&/@ Thread[{Prime[Range[Length[cmps]]], cmps}]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 21 2020 *)

CROSSREFS

Cf. A000040, A002808, A073459.

Sequence in context: A362367 A211661 A111972 * A194698 A105519 A111891

Adjacent sequences: A073455 A073456 A073457 * A073459 A073460 A073461

KEYWORD

nonn

AUTHOR

Labos Elemer, Aug 02 2002

STATUS

approved