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A258767 With a(1) = 1, a(n) is the smallest number not already in the sequence such that a(n)^2 + a(n-1)^2 is not squarefree.

%I A258767 #10 Jun 11 2015 17:40:25
%S A258767 1,7,14,2,4,3,6,8,10,5,12,9,13,16,18,15,20,21,22,11,23,36,24,26,28,29,
%T A258767 47,46,30,25,35,40,32,34,17,19,33,27,31,42,38,41,37,39,45,48,44,50,49,
%U A258767 43,51,54,52,56,58,59,62,60,55,65,70,63,57,66,64,68,72,69,67,81,75,78,71,53,79,97,96,74
%N A258767 With a(1) = 1, a(n) is the smallest number not already in the sequence such that a(n)^2 + a(n-1)^2 is not squarefree.
%C A258767 Believed to be a permutation of the natural numbers.
%H A258767 Reinhard Zumkeller, <a href="/A258767/b258767.txt">Table of n, a(n) for n = 1..10000</a>
%o A258767 (PARI) v=[1]; n=1; while(n<100, if(!issquarefree(n^2+v[#v]^2)&&!vecsearch(vecsort(v), n), v=concat(v, n); n=0); n++); v
%o A258767 (Haskell)
%o A258767 import Data.List (delete)
%o A258767 a258767 n = a258767_list !! (n-1)
%o A258767 a258767_list = 1 : f 1 [2..] where
%o A258767    f x zs = g zs where
%o A258767      g (y:ys) | a008966 (x^2 + y^2) == 1 = g ys
%o A258767               | otherwise = y : f y (delete y zs)
%o A258767 -- _Reinhard Zumkeller_, Jun 11 2015
%Y A258767 Cf. A256271, A075380.
%Y A258767 Cf. A258768 (fixed points).
%Y A258767 Cf. A008966, A258827 (putative inverse).
%K A258767 nonn
%O A258767 1,2
%A A258767 _Derek Orr_, Jun 09 2015