This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A078143 #23 Nov 05 2017 01:15:22
%S A078143 8870024,33908368,49250144,69147868,70918820,111500620,112931372,
%T A078143 164786748,167854344,200997948,203356712,207543320,211014920,
%U A078143 216785256,221167422,221167423,221167424,236645624,240574368,262315467,262315468
%N A078143 Smallest term of a run of at least 9 consecutive integers which are not squarefree.
%C A078143 The sequence includes an infinite family of arithmetic progressions. Such AP's can be constructed to each term, with large differences [like squares of primorials, A061742(7)]. It is necessary to solve suitable systems of linear Diophantine equations. E.g.: arithmetic progression subsequences of starting 9-chains is {mk+69147868+j} where j=0..8, m=510510^2 because square prime factors of a(4)+j=68147868+j are 4, 49, 121, 169, 4, 9, 289, 25, 4 resp. for j=0..8; k goes to infinity; 7th primorial is sufficient, 9th is not necessary. Construction is provable for arbitrary long [>9] chains. - _Labos Elemer_, Nov 25 2002
%C A078143 More precisely, if in one run {a(n)+j, j=0..8} the maximum smallest square factor is p^2, then an infinite subsequence is given by {a(n)+(p#)^2*k, k=0..oo}, where p# = A034386(p). One may get a smaller step taking the least L^2 which has a square factor in common with each of the 9 consecutive terms. - _M. F. Hasler_, Feb 03 2016
%H A078143 Donovan Johnson, <a href="/A078143/b078143.txt">Table of n, a(n) for n = 1..1000</a>
%F A078143 A078143 = { A077647[k] | A077647[k+1] = A077647[k]+1 } = { A077640[k] | A077640[k+2] = A077640[k]+2 } = { A078144[k] | A078144[k+4] = A078144[k]+4 } etc. Note that A049535 is defined differently. - _M. F. Hasler_, Feb 01 2016
%F A078143 a(n) < 4666864390*n. With more work this bound can be decreased significantly. - _Charles R Greathouse IV_, Nov 05 2017
%t A078143 s9[x_] := Apply[Plus, Table[Abs[MoebiusMu[x+j]], {j, 0, 8}]]; Do[If[Equal[s9[n], 0], Print[n]], {n, 8000000, 1000000000}]
%o A078143 (PARI) is(n)=for(i=n,n+8, if(!issquarefree(i), return(0))); 1 \\ _Charles R Greathouse IV_, Nov 05 2017
%Y A078143 Cf. A013929, A045882 (first of the k-chains), A051681.
%Y A078143 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), A268314 (11-chains).
%K A078143 nonn
%O A078143 1,1
%A A078143 _Labos Elemer_, Nov 22 2002
%E A078143 a(6)-a(21) from _Donovan Johnson_, Nov 26 2008