login
Number of primes between successive composite numbers.
5

%I #11 Apr 01 2021 13:18:54

%S 1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0,0,1,1,0,0,0,0,1,0,0,1,1,0,0,1,0,0,0,

%T 0,1,0,0,0,0,1,1,0,0,0,0,1,0,0,1,1,0,0,0,0,1,0,0,1,0,0,0,0,1,0,0,0,0,

%U 0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,1,1,0

%N Number of primes between successive composite numbers.

%H Harvey P. Dale, <a href="/A073784/b073784.txt">Table of n, a(n) for n = 1..1000</a>

%e a(7) = 0 since there are no primes between the 7th and the 8th composites (14 and 15).

%t Composite[n_Integer] := FixedPoint[n + PrimePi[ # ] + 1 &, n + PrimePi[n] + 1]; Table[ PrimePi[Composite[n + 1]] - PrimePi[Composite[n]], {n, 105}] (* _Robert G. Wilson v_, Dec 20 2004 *)

%t Differences[Select[Range[300],CompositeQ]]-1 (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Apr 01 2021 *)

%Y a(n) = A073783(n) - 1.

%Y a(n) = A002808(n+1) - A002808(n) - 1.

%Y Also first differences of A073425.

%K easy,nonn

%O 1,1

%A _Lior Manor_, Aug 11 2002