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

1,1

Comments

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

Links

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

Index entries for sequences that are permutations of the natural numbers

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A073846, A002808, A000040.

Sequence in context: A086305 A328047 A073898 * A073846 A110458 A217559

Adjacent sequences: A067744 A067745 A067746 * A067748 A067749 A067750

Keyword

easy,nonn

Author

Amarnath Murthy, Feb 26 2002

Status

approved