

A203069


Alternatingparity rearrangement of natural numbers: a(n) is the smallest number such that a(n1)+a(n) is odd and composite.


5



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

1,2


COMMENTS

Inspired by idea of Eric Angelini at SeqFan list Dec 28 2011.


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Éric Angelini, A December quiz with a nonprime array, SeqFan list, Dec 28 2011.
Index entries for sequences that are permutations of the natural numbers


EXAMPLE

a(1)=1; the smallest possible even number m such that 1+m is composite is m=8, hence a(2)=8;
the smallest possible odd number m such that 8+m is composite is m=7, hence a(3)=7;
the smallest possible even number m such that 7+m is composite is m=2, hence a(4)=2.


PROG

(Sage)
@cached_function
def A203069(n):
....if n == 1: return 1
....used = set(A203069(i) for i in [1..n1])
....works = lambda an: (A203069(n1)+an) % 2 == 1 and len(divisors((A203069(n1)+an))) > 2
....return next(k for k in PositiveIntegers() if k not in used and works(k)) # D. S. McNeil, Dec 28 2011
(Haskell)
import Data.List (delete)
a203069 n = a203069_list !! (n1)
a203069_list = 1 : f 1 [2..] where
f u vs = g vs where
g (w:ws)  odd z && a010051' z == 0 = w : f w (delete w vs)
 otherwise = g ws
where z = u + w
 Reinhard Zumkeller, Jan 14 2015


CROSSREFS

Cf. A010051, A249918 (inverse), A014076, A055266.
Sequence in context: A198928 A155068 A244839 * A272531 A244684 A201742
Adjacent sequences: A203066 A203067 A203068 * A203070 A203071 A203072


KEYWORD

nonn


AUTHOR

Zak Seidov, Dec 28 2011


STATUS

approved



