A223475 Least k such that the decimal representation of k*n has digits in nonincreasing order.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 4, 3, 2, 2, 3, 3, 4, 1, 1, 1, 4, 3, 2, 2, 2, 3, 3, 1, 1, 1, 1, 13, 2, 2, 2, 2, 17, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 15, 13, 9, 9, 1, 1, 1, 1, 1, 1, 1, 13, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 84, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 86, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 5, 7, 5, 2, 5, 3, 4, 6, 1, 1, 75, 47, 38, 8, 45, 56, 8, 7, 5, 55, 5, 7

Offset

1,12

Links

Giovanni Resta, Table of n, a(n) for n = 1..2000

Example

39*17 = 663 has digits in nonincreasing order, and no k < 17 has this property, hence a(39) = 17.

Mathematica

a[n_] := a[nn_] := Block[{n = nn, f, w = Range@9, k = 1}, While[Mod[n, 10] == 0, n /= 10]; While[(f = Select[w, Max@ Differences@ IntegerDigits[n*#] <= 0 &, 1]) == {}, k++; w = Union@ Flatten@Table[ Select[d*10^(k-1) + w, Max@ Differences@ IntegerDigits[Mod[n*#, 10^k], 10, k] <= 0 &], {d, 0, 9}]]; f[[1]]]; Array[a, 123] (* faster than basic approach. Giovanni Resta, Mar 26 2013 *)

Crossrefs

a(n)*n yields sequence A223474.

Cf. A079339, A181061.

Cf. A009996.

Sequence in context: A276373 A317173 A190302 * A190137 A003561 A201327

Adjacent sequences: A223472 A223473 A223474 * A223476 A223477 A223478

Keyword

nonn,base

Author

Paul Tek, Mar 20 2013

Status

approved