%I #16 Sep 08 2022 08:45:30

%S 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,

%T 41,24,43,25,47,26,53,27,59,28,61,30,67,32,71,33,73,34,79,35,83,36,89,

%U 38,97,39,101,40,103,42,107,44,109,45,113,46,127,48,131,49,137,50,139,51

%N Alternately write composite and prime numbers.

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

%F a(n) = A066249(n) + 1. - _Filip Zaludek_, Dec 10 2016

%e 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.

%t 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 *)

%o (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

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

%K nonn,easy

%O 1,1

%A _Edwin F. Sampang_, Mar 30 2007

%E Edited and extended by _Klaus Brockhaus_, Mar 31 2007