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

1,1

Comments

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

Links

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

Example

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).

Prog

(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
(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

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.

Sequence in context: A223320 A222280 A191560 * A253173 A195814 A165612

Adjacent sequences: A253169 A253170 A253171 * A253173 A253174 A253175

Keyword

nonn,easy,base

Author

Randy L. Ekl, Dec 28 2014

Status

approved