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 A078144 Starts for strings of at least five consecutive nonsquarefree numbers. 11
 844, 1680, 2888, 3624, 5046, 10924, 14748, 15848, 17404, 19940, 22020, 22021, 22624, 23272, 24647, 24648, 25772, 29348, 30248, 30923, 30924, 33172, 36700, 37248, 38724, 39444, 40472, 45372, 47672, 47673, 47724, 47824, 48372, 49488 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA A078144 = { A070284[k] | A070284[k+1] = A070284[k]+1 }. - M. F. Hasler, Feb 01 2016 a(n) = A188296(n) - 2. - Amiram Eldar, Feb 09 2021 EXAMPLE 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. MATHEMATICA s5[x_] := Total[Table[Abs[MoebiusMu[x + j]], {j, 0, 4}]] == 0; Select[Range[50000], s5] Flatten[Position[Partition[SquareFreeQ/@Range[60000], 5, 1], _?(Union[#] == {False}&), {1}, Heads->False]] (* Harvey P. Dale, May 24 2014 *) CROSSREFS 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. Sequence in context: A114359 A038013 A334183 * A071320 A338628 A323253 Adjacent sequences:  A078141 A078142 A078143 * A078145 A078146 A078147 KEYWORD nonn AUTHOR Labos Elemer, Nov 25 2002 STATUS approved

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Last modified January 18 09:26 EST 2022. Contains 350454 sequences. (Running on oeis4.)