

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
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OFFSET

1,2


COMMENTS

For k > 0: a(2*k1) + a(2*k) is prime, a(2*k) + a(2*k+1) is composite.


LINKS



FORMULA



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 !! (n1)
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



KEYWORD

nonn


AUTHOR



STATUS

approved



