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%I #6 Mar 15 2020 17:57:25
%S 551,989,1333,1363,5429,20081,26167,28381,28577,29719,60803,139163,
%T 147733,150047,161647,217103,224437,262921,293921,298007,302387,
%U 312913,342103,345127,385937,436129,508309,509189,539647,829921,873827,921391
%N Composite numbers not divisible by 7 which in base 7 contain their largest proper factor as a substring.
%t Do[ If[ !PrimeQ[ n ] && Mod[ n, 7 ] != 0 && StringPosition[ ToString[ FromDigits[ IntegerDigits[ n, 7 ] ] ], ToString[ FromDigits[ IntegerDigits[ Divisors[ n ][ [ -2 ] ], 7 ] ] ] ] != {}, Print[ n ] ], {n, 3, 10^6} ]
%t Select[Range[10^6],CompositeQ[#]&&Mod[#,7]!=0&&SequenceCount[ IntegerDigits[ #,7],IntegerDigits[Divisors[#][[-2]],7]]>0&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Mar 15 2020 *)
%K base,nonn
%O 1,1
%A _Robert G. Wilson v_, Aug 27 2001