A161811 Difference between nonprime(n+2) and nonprime(n).

4, 5, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 3, 2, 2, 2, 3, 4, 3, 2, 2, 2, 3, 3, 2, 3, 4, 3, 2, 3, 3, 2, 2, 2, 3, 3, 2, 2, 2, 3, 4, 3, 2, 2, 2, 3, 3, 2, 3, 4, 3, 2, 2, 2, 3, 3, 2, 3, 3, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 3, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 3, 3, 2, 2, 2, 3, 4

Offset: 1

Author

Juri-Stepan Gerasimov, Jun 20 2009

Keywords

• nonn

Comments

"nonprime(n)" is used for "n-th nonprime". Here the nonprimes start at 0 (see A141468), so nonprime(1) to nonprime(15) are 0, 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22.

Examples

			nonprime(1+2)-nonprime(1) = 4-0; so a(1) = 4.
nonprime(5+2)-nonprime(5) = 10-8; so a(5) = 2.
nonprime(11+2)-nonprime(11) = 20-16; so a(11) = 4.
		

Crossrefs

Cf. A031131, A141468.

Programs

Mathematica

#[[3]]-#[[1]]&/@Partition[Select[Range[0,150],!PrimeQ[#]&],3,1] (* Harvey P. Dale, Jul 08 2022 *)

Formula

a(n) = A141468(n+2)-A141468(n).

Extensions

Edited, corrected (a(11)=2 replaced by 4) and extended by Klaus Brockhaus, Jun 24 2009