A078144 - OEIS

A078144

Starts for strings of at least five consecutive nonsquarefree numbers.

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

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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 *)

SequencePosition[Table[If[SquareFreeQ[n], 0, 1], {n, 50000}], {1, 1, 1, 1, 1}][[All, 1]] (* Harvey P. Dale, Oct 16 2022 *)

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