A162154 Odd-indexed terms are the number of consecutive prime numbers until a composite, even-indexed terms are the number of consecutive composite numbers until a prime.

2, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 5, 1, 1, 1, 5, 1, 3, 1, 1, 1, 3, 1, 5, 1, 5, 1, 1, 1, 5, 1, 3, 1, 1, 1, 5, 1, 3, 1, 5, 1, 7, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 13, 1, 3, 1, 5, 1, 1, 1, 9, 1, 1, 1, 5, 1, 5, 1, 3, 1, 5, 1, 5, 1, 1, 1, 9, 1, 1, 1, 3, 1, 1, 1, 11, 1, 11, 1, 3, 1, 1, 1, 3, 1, 5, 1, 1, 1, 9

Offset: 1

Author

Claudio Meller, Jun 26 2009

Keywords

• nonn

Examples

			a(1)=2 because there are two consecutive primes (2 and 3), a(2)=1 (4);
a(5)=1 (7), a(6)=3 because there are three consecutive composite (8,9,10).
		

Links

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

Crossrefs

Cf. A046933.

Programs

Mathematica

Join[{2},Riffle[Last[#]-First[#]-1&/@Partition[Prime[Range[2,60]],2,1],1]] (* Harvey P. Dale, Jun 04 2012 *)

Formula

a(2n) = A046933(n+1). - R. J. Mathar, Jun 27 2009

a(2n+1) = 1, for n>=1. - Michel Marcus, Feb 21 2020

Extensions

Name edited by Michel Marcus, Feb 21 2020