|
Search: id:A078144
|
|
|
| A078144 |
|
Starts for strings of at least five consecutive non-square-free numbers. |
|
+0
2
|
|
| 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; listen)
|
|
|
OFFSET
|
1,1
|
|
|
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. quintette = {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_] := Apply[Plus, Table[Abs[MoebiusMu[x+j]], {j, 0, 4}]] If[Equal[s, 0], Print[n]], {n, 1, 1000000}]
|
|
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: A031707 A114359 A038013 this_sequence A071320 A127593 A085323
Adjacent sequences: A078141 A078142 A078143 this_sequence A078145 A078146 A078147
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Labos E. (labos(AT)ana.sote.hu), Nov 25 2002
|
|
|
Search completed in 0.002 seconds
|
