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A244724 Lexicographically earliest permutation of the natural numbers such that primes and composites alternate in the sums of adjacent terms. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 27 21:03 EST 2020. Contains 332309 sequences. (Running on oeis4.)