A206798 Beginning with the natural numbers, swap the k-th composite number (A002808) and k-th noncomposite number (A008578), for k = 1,2,3,...

4, 6, 8, 1, 9, 2, 10, 3, 5, 7, 12, 11, 14, 13, 17, 19, 15, 23, 16, 29, 31, 37, 18, 41, 43, 47, 53, 59, 20, 61, 21, 67, 71, 73, 79, 83, 22, 89, 97, 101, 24, 103, 25, 107, 109, 113, 26, 127, 131, 137, 139, 149, 27, 151, 157, 163, 167, 173, 28, 179, 30, 181, 191

Offset: 1

Author

Jaroslav Krizek, Feb 12 2012

Keywords

• nonn

Comments

Sequence is self-inverse permutation of natural numbers. Also swap sequence of pair of complements A002808 and A008578.

Examples

			a(7) = 10 becauce number 7 is 5th term of sequence A008578 and 5th term of sequence A002808 is number 10.
		

Crossrefs

Cf. A026234 (swap the k-th prime and k-th nonprime, for k = 1,2,3,...).

Programs

Mathematica

nn = 191; t1 = Select[Range[nn], # == 1 || PrimeQ[#] &]; t2 = Complement[Range[nn], t1]; t = Range[nn]; Do[temp = t[[t1[[i]]]]; t[[t1[[i]]]] = t[[t2[[i]]]]; t[[t2[[i]]]] = temp, {i, Length[t1]}]; Take[t, Position[t, t1[[-1]]][[1, 1]]] (* T. D. Noe, Feb 13 2012 *)

Formula

a(n) = A181097(n) for first 14 terms.