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a(n) is the smallest multiple of n whose decimal representation contains at least two digits which are the same.
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%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