A274328 - OEIS

%I #59 Mar 31 2018 10:59:00

%S 270,135,38475,252,1881,702,918,684,1656,2349,1953,7326,2952,2322,

%T 2961,3339,3717,3843,3015,3195,3285,5688,8217,5607,4365,95445,6489,

%U 4815,3924,37629,35433,10611,9864,5004,41571,4077,39564,2934,34569,42039

%N 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.

%C From _Ryan Hitchman_, Sep 15 2017: (Start)

%C a(172) = 1023847569, prime(172) = 1021 is the first entry with one multiple.

%C a(1884) = 145953, prime(1884) = 16217 is last with more than one multiple.

%C a(10545) = 0, prime(10545) = 111119 is the first zero. (End)

%H Ryan Hitchman, <a href="/A274328/b274328.txt">Table of n, a(n) for n = 1..10544</a>

%H Claudio Meller Blog, <a href="http://numbersandmath.blogspot.fr/2016/06/multiples-with-all-digits.html">Multiples with all the digits</a>, June 13 2016.

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

%t (m = Select[#*Range[10000], Max[DigitCount[#]] == 1 &];

%t    Total[m*LinearProgramming[m, Thread[DigitCount /@ m],

%t       ConstantArray[{1, 0}, 10], 0, Integers]]) & /@ Prime[Range[40]] (* _Ryan Hitchman_, Sep 15 2017 *)

%Y Cf. A180489 for n>1884. Superset of A050288. - _Ryan Hitchman_, Sep 15 2017

%K nonn,base

%O 1,1

%A _Claudio Meller_, Jun 21 2016

%E Terms a(9) and beyond, zero case from _Ryan Hitchman_, Sep 15 2017