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

Author

Reinhard Zumkeller, Jul 05 2014

Keywords

• nonn

Comments

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

Examples

			.             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 .
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

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

Programs

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

Formula

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