A244724 Lexicographically earliest permutation of the natural numbers such that primes and composites alternate in the sums of adjacent terms.

1, 2, 4, 3, 5, 6, 8, 9, 7, 10, 11, 12, 13, 16, 14, 15, 17, 20, 18, 19, 21, 22, 23, 24, 25, 28, 26, 27, 29, 30, 32, 35, 31, 36, 33, 34, 38, 41, 37, 42, 39, 40, 44, 45, 43, 46, 47, 50, 48, 49, 51, 52, 53, 54, 56, 57, 55, 58, 59, 68, 60, 67, 61, 66, 62, 65, 63

Offset

1,2

Comments

For k > 0: a(2*k-1) + a(2*k) is prime, a(2*k) + a(2*k+1) is composite.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers

Formula

A010051(a(n)+a(n+1)) = n mod 2.

Example

.             n | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
.          a(n) | 1 2 4 3 5 6 8 9 7 10 11 12 13 16 14 15 17 20 18 19
. A026233(a(n)) | 1 1 2 2 3 3 4 5 4  6  5  7  6 10  8  9  7 12 11  8 .

Prog

(Haskell)
import Data.List (delete)
a244724 n = a244724_list !! (n-1)
a244724_list = 1 : f 1 [2..] where
   f x xs = f' xs where
     f' (u:us) | a010051' (x + u) == 1 = g u (delete u xs)
               | otherwise             = f' us where
        g y ys = g' ys where
          g' (v:vs) | a010051' (y + v) == 0 = u : v : f v (delete v ys)
                    | otherwise        = g' vs

Crossrefs

Cf. A244732 (inverse), A244731 (fixed points), A073846, A113321, A115316.

Sequence in context: A105366 A077156 A258076 * A132948 A102569 A203554

Adjacent sequences: A244721 A244722 A244723 * A244725 A244726 A244727

Keyword

nonn

Author

Reinhard Zumkeller, Jul 05 2014

Status

approved