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%I #26 Jan 06 2024 14:32:35
%S 4,8,48,242,844,22020,217070,1092747,8870024,262315467,221167422,
%T 47255689915,82462576220,1043460553364,79180770078548,
%U 3215226335143218,23742453640900972,125781000834058568
%N Smallest term of first run of exactly n consecutive integers which are not squarefree.
%D a(16) was obtained as a result of a team effort by Z. McGregor-Dorsey et al.
%H L. Marmet, <a href="http://arxiv.org/abs/1210.3829">First occurrences of square-free gaps and an algorithm for their computation</a>, arXiv preprint arXiv:1210.3829 [math.NT], 2012. See also the <a href="http://www.marmet.org/louis/sqfgap/">author page</a>.
%H "sikefield3", <a href="https://github.com/sikefield3/double-square">double-square</a> (2019).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Squarefree.html">Squarefree</a>.
%e a(5) = 844: 844 = 2^2*211, 845 = 5*13^2, 846 = 2*3^2*47, 847 = 7*11^2, 848 = 2^4*53.
%t Module[{tb=Table[If[SquareFreeQ[n],0,1],{n,11*10^5}]},Table[ SequencePosition[ tb,PadRight[{},k,1],1][[All,1]],{k,8}]]//Flatten (* The program generates the first 8 terms of the sequence. To generate more, increase the constants for n and k but the program may take a long time to run. *) (* _Harvey P. Dale_, Mar 24 2022 *)
%o (PARI) iscons(x, n)=if (issquarefree(x-1) && issquarefree(x+n), for (k = 0, n-1, if (issquarefree(x+k), return (0));); return (1);); return (0);
%o a(n) = {my(x = 1); while (! iscons(x, n), x++); x;} \\ _Michel Marcus_, Jan 13 2014
%Y Cf. A045882 (another version), A013929, A053806.
%K nice,nonn,hard,more
%O 1,1
%A Louis Marmet (louis(AT)marmet.org) and David Bernier (ezcos(AT)yahoo.com)
%E a(16) reported by Louis Marmet (louis(AT)marmet.org), Jul 24 2000
%E a(17) was obtained as a result of a team effort by E. Wong et al.
%E a(18) = 125781000834058568 was obtained as a result of a team effort by L. Marmet et al.
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