%N a(1) = 1 and then alternately even and odd numbers not occurring earlier such that the sum of two successive terms is a squarefree number.
%C No string of 9 successive terms can be consecutive integers simply for one of the sums of pair of terms would be a multiple of 9=3^2. Conjecture: There are infinitely many strings of 8 terms of the form k,k+1,k+2,...k+7. Subsidiary sequences:(1) Start of the strings of 8 consecutive natural numbers. ( 5 more sequences),Start of the strings of r consecutive natural numbers for a particular r, 3<r<8.
%C A self-inverse permutation of the natural numbers.
%H Reinhard Zumkeller, <a href="/A077223/b077223.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o import Data.List (find, delete)
%o import Data.Maybe (fromJust)
%o a077223 n = a077223_list !! (n-1)
%o a077223_list = 1 : g 1 [2..] where
%o g i xs = x : g x (delete x xs) where
%o x = (fromJust $ find isOddSquarefree $ map (+ i)
%o isOddSquarefree m = odd m && a008966 m == 1
%o for_bFile = take 10000 a077223_list
%Y Cf. A008966.
%A _Amarnath Murthy_, Nov 03 2002
%E a(16)-a(71) from _Donovan Johnson_, Nov 17 2008