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%I #23 Oct 16 2022 10:30:05
%S 844,1680,2888,3624,5046,10924,14748,15848,17404,19940,22020,22021,
%T 22624,23272,24647,24648,25772,29348,30248,30923,30924,33172,36700,
%U 37248,38724,39444,40472,45372,47672,47673,47724,47824,48372,49488
%N Starts for strings of at least five consecutive nonsquarefree numbers.
%H Amiram Eldar, <a href="/A078144/b078144.txt">Table of n, a(n) for n = 1..10000</a>
%F A078144 = { A070284[k] | A070284[k+1] = A070284[k]+1 }. - _M. F. Hasler_, Feb 01 2016
%F a(n) = A188296(n) - 2. - _Amiram Eldar_, Feb 09 2021
%e Squares dividing 5-string=844+j, j=0,..,4 are as follows:4,169,9,121,16 resp. Each term initiates an arithmetic progression with suitable large difference. Such progressions are constructible by solving suitable linear Diophantine equations. E.g., quintet = {mk+3689649, mk+3689650, mk+3689651, mk+3689652, mk+3689653} = {9(592900k+409961, 25(213444k+147586, 49(108900k+75299, 4(1334025k+922413), 121(44100k+30493)}; m=2310*2310=A002110(5)^2=A061742(5)=5336100.
%t s5[x_] := Total[Table[Abs[MoebiusMu[x + j]], {j, 0, 4}]] == 0; Select[Range[50000], s5]
%t Flatten[Position[Partition[SquareFreeQ/@Range[60000],5,1],_?(Union[#] == {False}&),{1},Heads->False]] (* _Harvey P. Dale_, May 24 2014 *)
%t SequencePosition[Table[If[SquareFreeQ[n],0,1],{n,50000}],{1,1,1,1,1}][[All,1]] (* _Harvey P. Dale_, Oct 16 2022 *)
%Y Cf. A045882 (min terms), A068781 (2-chains), A070258 (3-chains), A070284 (4-chains), A078144 (5-chains), A049535 (6-chains), A077647 (8-chains), A078143 (9-chains), A188296.
%K nonn
%O 1,1
%A _Labos Elemer_, Nov 25 2002
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