

A274328


a(n) is the sum of a sequence of multiples of the nth prime such that it contains each of the digits from 0 to 9 exactly once and with the least sum possible, or 0 if there is no satisfying sequence.


4



270, 135, 38475, 252, 1881, 702, 918, 684, 1656, 2349, 1953, 7326, 2952, 2322, 2961, 3339, 3717, 3843, 3015, 3195, 3285, 5688, 8217, 5607, 4365, 95445, 6489, 4815, 3924, 37629, 35433, 10611, 9864, 5004, 41571, 4077, 39564, 2934, 34569, 42039
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OFFSET

1,1


COMMENTS

From Ryan Hitchman, Sep 15 2017: (Start)
a(172) = 1023847569, prime(172) = 1021 is the first entry with one multiple.
a(1884) = 145953, prime(1884) = 16217 is last with more than one multiple.
a(10545) = 0, prime(10545) = 111119 is the first zero. (End)


LINKS

Ryan Hitchman, Table of n, a(n) for n = 1..10544
Claudio Meller Blog, Multiples with all the digits, June 13 2016.


EXAMPLE

For n = 7, a(7) = 918 because prime(7) = 17, sequence 34, 85, 102, 697, sum 918.


MATHEMATICA

(m = Select[#*Range[10000], Max[DigitCount[#]] == 1 &];
Total[m*LinearProgramming[m, Thread[DigitCount /@ m],
ConstantArray[{1, 0}, 10], 0, Integers]]) & /@ Prime[Range[40]] (* Ryan Hitchman, Sep 15 2017 *)


CROSSREFS

Cf. A180489 for n>1884. Superset of A050288.  Ryan Hitchman, Sep 15 2017
Sequence in context: A166807 A131264 A053322 * A025393 A291790 A025394
Adjacent sequences: A274325 A274326 A274327 * A274329 A274330 A274331


KEYWORD

nonn,base


AUTHOR

Claudio Meller, Jun 21 2016


EXTENSIONS

Terms a(9) and beyond, zero case from Ryan Hitchman, Sep 15 2017


STATUS

approved



