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A266586 The least nonnegative integer N such that n*N has the same digits as n and N together, not counting repetitions. 3
1, 6163, 51, 416, 251, 21, 967, 86, 255, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1255, 1, 781, 973, 26, 265, 24, 81, 1139, 1135, 51, 1, 291, 186, 151, 41, 936, 3001, 886, 982, 416, 1, 341, 315, 1464, 181, 734, 371, 958, 1921, 251, 1, 2412, 635, 846, 221, 1801, 125, 948, 845, 21, 1, 251, 585, 2213, 281, 1076 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A266578 for the variant where repeated digits are counted.

a(n) = 1 for 100 <= n <= 199 (and whenever n has a digit 1, cf. A011531), but then the sequence continues nontrivially with a(200,...) = (1255, 1, 751, 621, 251, 99, 511, 97, 101, 101, ...).

Record values are a(2) = 6163, a(2953) = 6521, a(3597) = 7209, a(5904) = 8047, a(23222) = 7681, a(39808) = 8011, a(39993) = 8231, a(44444) = 10151, ...

For small k=1,...,6, the graphs over the range 1 .. 10^(k+1) are roughly ("self"-)similar, because of the ranges 10^k .. 2*10^k-1 and (m+1/10)*10^k .. (m+2/10)*10^k-1 (with m=2,...,9) etc., on which a(n) = 1, while generically a(n) has values ranging quite uniformly between 1 and 10^4. For larger k, the picture changes, since pandigital numbers (and therefore also numbers having a digit '1') have asymptotic density one.

LINKS

M. F. Hasler, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = 1 whenever n has a digit '1', i.e., n in A011531.

a(n) <= A266578(n) unless A266578(n) = 0.

EXAMPLE

a(2) = 6163 since 2*6163 = 12326 has the same digits (1, 2, 3 and 6) as concat(2,6163) = 26163, and 6163 is the least N with this property.

MAPLE

f:= proc(n) local k, Ln, Lk, Lnk;

  Ln:= convert(convert(n, base, 10), set);

  if has(Ln, 1) then return 1 fi;

  for k from 2 do

    Lk:= convert(convert(k, base, 10), set);

    Lnk:= convert(convert(n*k, base, 10), set);

    if Lnk = Ln union Lk then return k fi

  od

end proc:

map(f, [$1..100]); # Robert Israel, Jan 01 2016

PROG

(PARI) A266586(n, L=9e9, d=digits(n))=for(k=1, L, Set(digits(k*n))==Set(concat(digits(k), d))&&return(k))

CROSSREFS

Cf. A266578, A266798.

Sequence in context: A281265 A007992 A033288 * A057880 A151967 A214556

Adjacent sequences:  A266583 A266584 A266585 * A266587 A266588 A266589

KEYWORD

nonn,base

AUTHOR

M. F. Hasler, Jan 01 2016

STATUS

approved

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Last modified February 23 07:06 EST 2018. Contains 299473 sequences. (Running on oeis4.)