A067747 Primes interleaved between composite numbers: n-th prime followed by the n-th composite number.

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

Offset: 1

Author

Amarnath Murthy, Feb 26 2002

Keywords

• easy
• nonn

Comments

a(2*n-1) = A000040(n); a(2*n) = A002808(n). - Reinhard Zumkeller, Jan 29 2014

Examples

			For n=4, the index is even. Therefore a(4)=A002808(4/2)=A002808(2)=6.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000.
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A073846, A002808, A000040.

Programs

Haskell

import Data.List (transpose)
a067747 n = a067747_list !! (n-1)
a067747_list = concat $ transpose [a000040_list, a002808_list]
-- Reinhard Zumkeller, Jan 29 2014

Maple

P,C:= selectremove(isprime,[$2..1000]):
seq(op([P[i],C[i]]),i=1..min(nops(P),nops(C))); # Robert Israel, Jul 24 2015

Mathematica

Array[c,1000];pc=-1;nc=0;Do[If[PrimeQ[n],If[pc==999,Break[],pc+=2;c[pc]=n],If[nc<=998,nc+=2;c[nc]=n,Goto[ne]]];Label[ne],{n,2,20000}];Table[c[i],{i,1000}] (* Zak Seidov, Mar 22 2008 *)
Composite[n_Integer] := FixedPoint[n + PrimePi@ # + 1 &, n + PrimePi@ n + 1]; Table[{Prime@ n, Composite@ n}, {n, 35}] // Flatten (* Robert G. Wilson v, Jun 08 2008 *)

PARI

c(n) = for(k=0, primepi(n), isprime(n++)&&k--); n; \\ A002808
a(n) = if (n%2, prime((n+1)/2), c((n+1)\2)); \\ Michel Marcus, Mar 06 2021

Formula

a(2*n-1) = A000040(n); a(2*n) = A002808(n). - Reinhard Zumkeller, Jan 29 2014

a(n) = A000040(ceiling(n/2))*A000035(n) + A002808(ceiling(n/2))*A059841(n), equivalent to the Zumkeller formula. - Chayim Lowen, Jul 29 2015