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%I #20 Jan 07 2024 22:09:45
%S 1,2,3,4,6,5,8,7,10,9,12,11,15,14,16,13,17,18,19,20,21,22,24,23,28,25,
%T 26,27,30,29,32,33,34,31,35,36,37,40,38,39,43,42,41,44,45,46,47,48,49,
%U 52,50,51,54,53,56,55,58,57,61,62,60,59,63,64,65,66,67,70,68,69,72,71
%N a(1)=1. a(n) = the smallest positive integer not occurring earlier in the sequence such that a(n-1)+a(n) is squarefree.
%C Inverse: A167905; A167904(n) = a(a(n)). [_Reinhard Zumkeller_, Nov 15 2009]
%C Conjectured to be a permutation of the natural numbers. - _Derek Orr_, Jun 01 2015
%H Scott R. Shannon, <a href="/A121878/b121878.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> [_Reinhard Zumkeller_, Nov 15 2009]
%e 9,10,11,12,... are the positive integers not occurring among the first 8 terms of the sequence. a(8) + 9 = 16, which is not squarefree. a(8) + 10 = 17, which is squarefree. So a(9) = 10.
%t f[s_] := Block[{k = 1},While[MemberQ[s, k] || Max @@ Last /@ FactorInteger[(s[[ -1]] + k)] > 1, k++ ]; Append[s, k]]; Nest[f, {1}, 75] (* _Ray Chandler_, Sep 06 2006 *)
%o (PARI) v=[1];n=1;while(n<100,if(issquarefree(v[#v]+n)&&!vecsearch(vecsort(v),n),v=concat(v,n);n=0);n++);v \\ _Derek Orr_, Jun 01 2015
%Y Cf. A167907, A075380. [_Reinhard Zumkeller_, Nov 15 2009]
%K nonn
%O 1,2
%A _Leroy Quet_, Aug 31 2006
%E Extended by _Ray Chandler_, Sep 06 2006
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