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

Author

Claudio Meller, Jun 21 2016

Keywords

• nonn
• base

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)

Examples

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

Links

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

Crossrefs

Cf. A180489 for n>1884. Superset of A050288. - Ryan Hitchman, Sep 15 2017

Programs

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 *)

Extensions

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