A337240 a(n) is the smallest multiple of n whose decimal representation contains at least two digits which are the same.

11, 22, 33, 44, 55, 66, 77, 88, 99, 100, 11, 144, 117, 112, 225, 112, 119, 144, 114, 100, 252, 22, 115, 144, 100, 338, 999, 112, 116, 300, 155, 224, 33, 272, 455, 144, 111, 114, 117, 200, 533, 252, 344, 44, 225, 322, 141, 144, 343, 100, 255, 676, 212, 1080, 55

Offset

1,1

Links

Table of n, a(n) for n=1..55.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

a(n) = n*A337241(n).

a(n) = n for any n >= 10^10. - Rémy Sigrist, Sep 15 2020

Example

a(13) = 117 because 117 is the smallest multiple of 13 with equal digits.
a(16) = 112 because 112 is the smallest multiple of 16 with equal digits.
a(25) = 100 because 100 is the smallest multiple of 25 with equal digits.

Mathematica

Array[Block[{k = 1}, While[NoneTrue[DigitCount[k #], # > 1 &], k++]; k #] &, 55] (* Michael De Vlieger, Aug 21 2020 *)

Prog

(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

Crossrefs

Cf. A045538 (least k such that k*n contains two equal consecutive digits).

Cf. A337241 (least k such that k*n contains two equal digits).

Sequence in context: A367610 A087346 A060314 * A109303 A338214 A068520

Adjacent sequences: A337237 A337238 A337239 * A337241 A337242 A337243

Keyword

nonn,base

Author

Rodolfo Kurchan, Aug 20 2020

Status

approved