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A067747 Primes interleaved between composite numbers: n-th prime followed by the n-th composite number. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
a(2*n-1) = A000040(n); a(2*n) = A002808(n). - Reinhard Zumkeller, Jan 29 2014
LINKS
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
Sequence in context: A086305 A328047 A073898 * A073846 A110458 A217559
KEYWORD
easy,nonn
AUTHOR
Amarnath Murthy, Feb 26 2002
STATUS
approved

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Last modified April 17 15:33 EDT 2024. Contains 371764 sequences. (Running on oeis4.)