A026234 In the sequence of positive integers, swap the k-th prime and k-th nonprime, for k = 1,2,3,...

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

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

A permutation of the positive integers. - M. F. Hasler, Jan 29 2014

Examples

			a(1) = 2 because 1 is not prime and the first prime is 2.
a(2) = 1 because 2 is prime and the first nonprime is 1.
a(3) = 4 because 3 is prime and the second nonprime is 4.
a(4) = 3 because 4 is not prime and the second prime is 3.
a(5) = 6 because 5 is prime and the third nonprime is 6.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000.

Crossrefs

Cf. A236675, A236676.

Programs

Mathematica

nonPrimePi[n_] := n - PrimePi[n]; nonPrime[n_] := FixedPoint[n + PrimePi[#] &, n + PrimePi[n]]; A026234[n_] := If[PrimeQ[n], nonPrime[PrimePi[n]], Prime[nonPrimePi[n]]]; Table[A026234[n], {n, 200}] (* Enrique Pérez Herrero, Jan 28 2014 *)

PARI

c=p=0;vector(99,n,if(isprime(n),while(isprime(c++),);c,prime(p++))) \\ M. F. Hasler, Jan 29 2014

PARI

A026234 = n->if(isprime(n),A018252(primepi(n)),prime(n-primepi(n))) \\ M. F. Hasler, Jan 29 2014

Formula

If n is prime, then a(n) = A018252(n), else a(n) = A000040(n). - M. F. Hasler, Jan 29 2014