A274328 a(n) is the sum of a sequence of multiples of the n-th 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.

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

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