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A253172 Numbers n = p * q, where n, p, and q together contain all 10 digits at least once.

%I A253172 #21 Dec 30 2014 09:47:04
%S A253172 15628,15678,16038,17082,17820,19084,20457,20748,20754,21658,24507,
%T A253172 24587,25704,26910,26970,27096,27504,27690,28156,28651,29076,29370,
%U A253172 29670,29706,29730,30956,30972,30976,32890,32970,34056,34902,34986,35046,35074,35096,35496,35690,36092,36490,36508,36950,36970,36972,37092,37096,37290,37590,37690,37908,38870,39026,39720,39760,40587,40596
%N A253172 Numbers n = p * q, where n, p, and q together contain all 10 digits at least once.
%C A253172 All pandigital numbers (cf. A171102) belong to this sequence; therefore A050288(1) = 10123457689 is the smallest prime term. - _Reinhard Zumkeller_, Dec 29 2014
%H A253172 Reinhard Zumkeller, <a href="/A253172/b253172.txt">Table of n, a(n) for n = 1..1000</a>
%e A253172 a(1) is 15628 = 4 * 3907, using all 10 digits.
%e A253172 a(8) is 20748 = 13 * 1596 (note duplicate 1, which is ok in this sequence).
%e A253172 a(3) is 16038 = 27 * 594, and also 16038 = 54 * 297; two different solutions for a(3).
%o A253172 (PARI) isokpq(n) = {fordiv(n, d, digs = digits(n); if ( d <= sqrtint(n), digs = concat(digs, digits(d)); digs = concat(digs, digits(n/d)); if (#Set(digs) == 10, return(1));););}
%o A253172 lista(nn) = {for(n=2, nn, if (isokpq(n), print1(n, ", ")););} \\ _Michel Marcus_, Dec 29 2014
%o A253172 (Haskell)
%o A253172 import Data.List (nub, sort)
%o A253172 a253172 n = a253172_list !! (n-1)
%o A253172 a253172_list = filter f [2..] where
%o A253172    f x = g divs $ reverse divs where
%o A253172          g (d:ds) (q:qs) = d <= q &&
%o A253172            (sort (nub $ xs ++ show d ++ show q) == decs || g ds qs)
%o A253172          xs = show x
%o A253172          divs = a027750_row x
%o A253172    decs = "0123456789"
%o A253172 -- _Reinhard Zumkeller_, Dec 29 2014
%Y A253172 Cf. A195814, which restricts sequence terms along with their factors to exactly 10 digits, and thus has a finite number of terms.
%Y A253172 Cf. A027750, subsequences: A050278, A171102, A050288.
%K A253172 nonn,easy,base
%O A253172 1,1
%A A253172 _Randy L. Ekl_, Dec 28 2014