A026239 Beginning with the natural numbers, swap the k-th prime and k-th composite.

1, 4, 6, 2, 8, 3, 9, 5, 7, 11, 10, 13, 12, 17, 19, 23, 14, 29, 15, 31, 37, 41, 16, 43, 47, 53, 59, 61, 18, 67, 20, 71, 73, 79, 83, 89, 21, 97, 101, 103, 22, 107, 24, 109, 113, 127, 25, 131, 137, 139, 149, 151, 26, 157, 163, 167, 173, 179, 27, 181, 28, 191, 193, 197, 199

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Comments

Involution (self-inverse permutation) of [positive] natural numbers.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A236854.

Programs

Haskell

a026239 1 = 1
a026239 n | a010051 n == 1 = a002808 $ a049084 n
          | otherwise      = a000040 $ a066246 n
-- Reinhard Zumkeller, Mar 30 2014

Mathematica

Composite[n_Integer] := FixedPoint[n + PrimePi@# + 1 &, n + PrimePi@n + 1]; f[1] = 1; f[n_] := If[ PrimeQ@n, Composite@ PrimePi@n, Prime[n - 1 - PrimePi@n]]; Array[f, 65] (* Robert G. Wilson v, Jun 08 2010 *)

Formula

a(1) = 1 and a(n) = if n is prime then A002808(A049084(n)) else A000040(A066246(n)) for n>1. - Reinhard Zumkeller, Dec 13 2001

Extensions

More terms from Robert G. Wilson v, Jun 08 2010