A244724 - OEIS

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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 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,2`
	COMMENTS	`For k > 0: a(2k-1) + a(2k) is prime, a(2k) + a(2k+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 March 20 22:57 EDT 2023. Contains 361392 sequences. (Running on oeis4.)