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A253172 Numbers n = p * q, where n, p, and q together contain all 10 digits at least once. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 21 17:55 EDT 2017. Contains 290893 sequences.