A337241 a(n) is the least k such that the decimal representation of k*n contains at least two digits which are the same.

11, 11, 11, 11, 11, 11, 11, 11, 11, 10, 1, 12, 9, 8, 15, 7, 7, 8, 6, 5, 12, 1, 5, 6, 4, 13, 37, 4, 4, 10, 5, 7, 1, 8, 13, 4, 3, 3, 3, 5, 13, 6, 8, 1, 5, 7, 3, 3, 7, 2, 5, 13, 4, 20, 1, 2, 2, 2, 2, 5, 2, 7, 4, 7, 7, 1, 5, 4, 6, 10, 5, 2, 4, 3, 3, 3, 1, 11, 6, 5, 14, 8, 2, 3, 3

Offset

1,1

Comments

First differs from A045538 at a(21) = 12 since 21 * 12 = 252 contains two equal but not consecutive digits. A045538(21) = 16.

The largest value is a(27)=37. - Robert Israel, Sep 17 2020

Links

Robert Israel, Table of n, a(n) for n = 1..10000

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

Formula

a(n) <= A045538(n).

a(n) = 1 for any n >= 10^10. - Rémy Sigrist, Sep 15 2020

Example

a(21) = 12 because 21*12 = 252 is the smallest multiple of 21 with equal digits.
a(23) = 5 because 23*5 = 115 is the smallest multiple of 23 with equal digits.
a(34) = 8 because 34*8 = 272 is the smallest multiple of 34 with equal digits.

Maple

f:= proc(n) local k, L;
  for k from 1 do
    L:= convert(k*n, base, 10);
    if nops(convert(L, set))<nops(L) then return k fi
  od;
end proc:
map(f, [$1..100]); # Robert Israel, Sep 17 2020

Mathematica

a[n_] := Module[{k = 1}, While[Max@ (Last /@ Tally @ IntegerDigits[k*n]) == 1, k++]; k]; Array[a, 100] (* Amiram Eldar, Aug 22 2020 *)

Prog

(PARI) a(n) = {my(k=1, d=digits(n)); while(#Set(d) == #d, k++; d=digits(k*n)); k; } \\ Michel Marcus, Aug 22 2020

Crossrefs

Cf. A045538 (where the 2 digits must be consecutive), A337240 (resulting k*n).

Sequence in context: A087994 A100755 A171902 * A045538 A084066 A231472

Adjacent sequences: A337238 A337239 A337240 * A337242 A337243 A337244

Keyword

nonn,base

Author

Rodolfo Kurchan, Aug 20 2020

Status

approved