A268314 First term of a run of at least 11 consecutive integers which are not squarefree.

221167422, 1407472722, 3639720042, 3865964268, 4982931368, 5005996146, 7108776620, 8044261244, 10249558974, 12766690268, 13585489166, 19792784322, 26995377572, 30410811296, 30477326444, 32070270968, 34317891368, 39956560824, 40841363528, 42216508746, 43133805944, 46295514872, 47255689915

Offset: 1

Author

M. F. Hasler, Feb 01 2016

Keywords

• nonn

Comments

a(23) is the first term beginning a 12-chain. - Bill Hannaford, Oct 06 2016

Crossrefs

Cf. A013929, A045882 (first of the k-chains), A051681.

Cf. A068781 (2-chains), A070258 (3-chains), A070284 (4-chains), A078144 (5-chains), A049535 (6-chains), A077640 (7-chains), A077647 (8-chains), A078143 (9-chains), A268313 (10-chains).

Programs

Mathematica

s11[x_] := Apply[Plus, Table[Abs[MoebiusMu[x+j]], {j, 0, 10}]]; Do[If[Equal[s11[n], 0], Print[n]], {n, 10^8, 10^13}]

Formula

A268314 = { A268313[k] | A268313[k+1] = A268313[k]+1 } = { A078143[k] | A078143[k+2] = A078143[k]+2 } = { A077647[k] | A077647[k+3] = A077647[k]+3 } = { A077640[k] | A077640[k+4] = A077640[k]+4 }.

Extensions

a(12)-a(23) from Bill Hannaford, Oct 06 2016