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

15628, 15678, 16038, 17082, 17820, 19084, 20457, 20748, 20754, 21658, 24507, 24587, 25704, 26910, 26970, 27096, 27504, 27690, 28156, 28651, 29076, 29370, 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

Offset: 1

Author

Randy L. Ekl, Dec 28 2014

Keywords

• nonn
• easy
• base

Comments

All pandigital numbers (cf. A171102) belong to this sequence; therefore A050288(1) = 10123457689 is the smallest prime term. - Reinhard Zumkeller, Dec 29 2014

Examples

			a(1) is 15628 = 4 * 3907, using all 10 digits.
a(8) is 20748 = 13 * 1596 (note duplicate 1, which is ok in this sequence).
a(3) is 16038 = 27 * 594, and also 16038 = 54 * 297; two different solutions for a(3).
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A195814, which restricts sequence terms along with their factors to exactly 10 digits, and thus has a finite number of terms.

Cf. A027750, subsequences: A050278, A171102, A050288.

Programs

Haskell

import Data.List (nub, sort)
a253172 n = a253172_list !! (n-1)
a253172_list = filter f [2..] where
   f x = g divs $ reverse divs where
         g (d:ds) (q:qs) = d <= q &&
           (sort (nub $ xs ++ show d ++ show q) == decs || g ds qs)
         xs = show x
         divs = a027750_row x
   decs = "0123456789"
-- Reinhard Zumkeller, Dec 29 2014

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));););}
lista(nn) = {for(n=2, nn, if (isokpq(n), print1(n, ", ")););} \\ Michel Marcus, Dec 29 2014