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

Author

Paul Tek, Mar 20 2013

Keywords

• nonn
• base

Examples

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

Links

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

Crossrefs

a(n)*n yields sequence A223474.

Cf. A079339, A181061.

Cf. A009996.

Programs

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 *)