A073784 Number of primes between successive composite numbers.

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, 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, 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

Offset: 1

Author

Lior Manor, Aug 11 2002

Keywords

• easy
• nonn

Examples

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

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

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

Also first differences of A073425.

Programs

Mathematica

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