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%I #13 Jun 11 2015 09:36:21
%S 1,2,3,5,4,7,6,11,8,9,10,13,12,17,14,15,16,19,18,23,20,27,22,25,21,26,
%T 29,24,31,28,33,32,35,34,39,38,37,30,41,36,43,40,47,42,53,44,45,46,49,
%U 48,59,50,51,52,55,54,61,56,57,58,63,62,65,64,67,60,71,66,73,68,69,70,79,74,75,76,77,72,83,78,85
%N a(1) = 1; for n > 1, a(n) is the smallest number not already in the sequence such that a(n)^2 + a(n-1)^2 is squarefree.
%C This is conjectured to be a permutation of the natural numbers.
%H Giovanni Resta, <a href="/A256271/b256271.txt">Table of n, a(n) for n = 1..10000</a>
%t a={1}; While[Length[a]<1000, e=Last@a; s = Select[ Complement[ Range@e, a], SquareFreeQ[e^2 + #^2]&, 1]; If[s!={}, s=s[[1]], s=e+1; While[ MemberQ[a, s] || !SquareFreeQ[ e^2 + s^2], s++]]; AppendTo[a, s]]; a (* first 1000 terms, _Giovanni Resta_, Jun 02 2015 *)
%o (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
%Y Cf. A121878, A256270.
%K nonn,easy
%O 1,2
%A _Derek Orr_, Jun 01 2015