%I #27 Sep 16 2020 02:22:13
%S 11,22,33,44,55,66,77,88,99,100,11,144,117,112,225,112,119,144,114,
%T 100,252,22,115,144,100,338,999,112,116,300,155,224,33,272,455,144,
%U 111,114,117,200,533,252,344,44,225,322,141,144,343,100,255,676,212,1080,55
%N a(n) is the smallest multiple of n whose decimal representation contains at least two digits which are the same.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n) = n*A337241(n).
%F a(n) = n for any n >= 10^10. - _Rémy Sigrist_, Sep 15 2020
%e a(13) = 117 because 117 is the smallest multiple of 13 with equal digits.
%e a(16) = 112 because 112 is the smallest multiple of 16 with equal digits.
%e a(25) = 100 because 100 is the smallest multiple of 25 with equal digits.
%t Array[Block[{k = 1}, While[NoneTrue[DigitCount[k #], # > 1 &], k++]; k #] &, 55] (* _Michael De Vlieger_, Aug 21 2020 *)
%o (PARI) a(n) = {my(k=1, d=digits(n)); while(#Set(d) == #d, k++; d=digits(k*n)); k*n;} \\ _Michel Marcus_, Aug 22 2020
%Y Cf. A045538 (least k such that k*n contains two equal consecutive digits).
%Y Cf. A337241 (least k such that k*n contains two equal digits).
%K nonn,base
%O 1,1
%A _Rodolfo Kurchan_, Aug 20 2020