A273260 - OEIS

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.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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

LINKS

Hans Havermann, Table of n, a(n) for n = 1..13100

Hans Havermann, A factorization balancing act

EXAMPLE

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.

CROSSREFS

Cf. A057885, A124668, A195814.

Sequence in context: A292701 A275417 A206539 * A015303 A236622 A329785

Adjacent sequences: A273257 A273258 A273259 * A273261 A273262 A273263

KEYWORD

nonn,base

AUTHOR

Hans Havermann, Aug 28 2016

STATUS

approved