A129131 Alternately write composite and prime numbers.

4, 2, 6, 3, 8, 5, 9, 7, 10, 11, 12, 13, 14, 17, 15, 19, 16, 23, 18, 29, 20, 31, 21, 37, 22, 41, 24, 43, 25, 47, 26, 53, 27, 59, 28, 61, 30, 67, 32, 71, 33, 73, 34, 79, 35, 83, 36, 89, 38, 97, 39, 101, 40, 103, 42, 107, 44, 109, 45, 113, 46, 127, 48, 131, 49, 137, 50, 139, 51

Offset: 1

Author

Edwin F. Sampang, Mar 30 2007

Keywords

• nonn
• easy

Comments

a(2n-1) = A073846(2n+1), a(2n) = A073846(2n).

Examples

			Lowest composite number is 4, lowest prime number is 2, next composite number after 4 is 6, next prime number after 2 is 3 and so on.
		

Crossrefs

Cf. A000040 (prime numbers), A002808 (composite numbers), A073846 (alternate nonprime and prime numbers).

Programs

Magma

P:=[ n : n in [2..150] | IsPrime(n) ]; C:=[ n : n in [2..70] | not IsPrime(n) ]; &cat[ [C[k], P[k] ]: k in [1..Minimum(#C, #P)] ]; // Klaus Brockhaus, Mar 31 2007

Mathematica

f[n_]:=Module[{prs=Prime[Range[n]],comps},comps=Rest[Complement[Range[n+ Length[prs]+1], prs]];Riffle[comps,prs]] (* Harvey P. Dale, May 10 2011 *)

Formula

a(n) = A066249(n) + 1. - Filip Zaludek, Dec 10 2016

Extensions

Edited and extended by Klaus Brockhaus, Mar 31 2007