A195814 -id:A195814 - cp's OEIS frontend

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

Randy L. Ekl, Dec 28 2014

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

			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).

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

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.

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

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

A273260 List of base-ten k-balanced factorization integers: The combined digits of an integer and its factorization primes and exponents contain exactly k copies of each of the ten digits, for some k.

Original entry on oeis.org

26487, 28651, 61054, 65821, 45849660, 84568740, 104086845, 106978404, 107569740, 107804658, 108489045, 118678440, 130445658, 130567806, 135807860, 137678445, 140679804, 140884695, 143450660, 143976180, 146859800, 148478520, 149528648, 150468056, 150568824

Offset: 1

Hans Havermann, Aug 28 2016

The b-file includes the smallest 74 k=3 integers but is still missing the largest 3 k=2 integers, which are 3392164558027, 8789650571264, and 9418623046875. - Hans Havermann, Jan 20 2017

			There are exactly four terms with k=1, namely the first four terms on the list: 26487 = 3^5*109, 28651 = 7*4093, 61054 = 2*7^3*89, and 65821 = 7*9403. In each of these, the digits of the number and the digits on the right-hand side of the equals sign together consist exactly of the digits 0 through 9.
8789650571264 is in the sequence because its digits combined with the digits of 2^31*4093 contain exactly two of every base ten digit.

Hans Havermann, Table of n, a(n) for n = 1..13100
Hans Havermann, A factorization balancing act

Cf. A057885, A124668, A195814.

A253173 Values n, where n = p * q, and n, p, and q together contain all 10 digits at least once, and no digit is in more than one of n, p or q.

Original entry on oeis.org

15628, 15678, 16038, 17082, 17820, 19084, 20457, 20754, 21658, 24507, 26910, 27504, 28156, 28651, 30976, 32890, 34902, 35046, 35496, 36508, 36970, 37096, 37690, 38870, 40596, 40898, 43076, 43670, 45068, 46740, 46970, 47690, 48504, 48592, 50076, 50346

Offset: 1

Randy L. Ekl, Dec 28 2014

			a(1) is 15628 = 4 * 3907, using all 10 digits.
20748 = 13 * 1596, using all 10 digits, but is NOT a member of this sequence, because the digit 1 appears in both p and q.

Cf. A195814 (a finite subsequence).

Cf. A253172 (a supersequence, which allows for duplicate digits in n, p and q).

isok(n) = {fordiv(n, d, q = n/d; sn = vecsort(digits(n),,8); sd = vecsort(digits(d),,8); sq = vecsort(digits(q),,8); sa = vecsort(concat(sn, concat(sd, sq)),,8); if ((#sa == 10) && (#sn + #sd + #sq == 10), return (1));); return (0);} \\ Michel Marcus, Feb 07 2015

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

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A273260 List of base-ten k-balanced factorization integers: The combined digits of an integer and its factorization primes and exponents contain exactly k copies of each of the ten digits, for some k.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A253173 Values n, where n = p * q, and n, p, and q together contain all 10 digits at least once, and no digit is in more than one of n, p or q.

Views

Author

Keywords

Examples

Crossrefs

Programs

PARI