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A078144 Starts for strings of at least five consecutive nonsquarefree numbers. 10
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

Table of n, a(n) for n=1..34.

FORMULA

A078144 = { A070284[k] | A070284[k+1] = A070284[k]+1 }. - M. F. Hasler, Feb 01 2016

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].

Sequence in context: A158403 A114359 A038013 * A071320 A160212 A188296

Adjacent sequences:  A078141 A078142 A078143 * A078145 A078146 A078147

KEYWORD

nonn

AUTHOR

Labos Elemer, Nov 25 2002

STATUS

approved

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Last modified August 23 01:14 EDT 2017. Contains 290953 sequences.