A273040 Least k >= 2 such that the base-k digits of n are nondecreasing.

2, 3, 2, 3, 3, 4, 2, 3, 5, 4, 4, 5, 3, 3, 2, 6, 3, 5, 5, 7, 4, 4, 4, 5, 7, 3, 4, 6, 6, 8, 2, 5, 5, 5, 6, 8, 5, 5, 5, 3, 3, 4, 4, 3, 6, 6, 4, 7, 5, 6, 6, 6, 3, 8, 8, 10, 6, 6, 6, 7, 7, 5, 2, 5, 6, 7, 7, 5, 5, 9, 6, 11, 7, 5, 7, 7, 8, 8, 8, 3, 7, 7, 7, 8, 4

Offset: 1

Author

Robert Israel, May 13 2016

Keywords

• nonn
• base

Comments

a(n) = 2 iff n is in A000225.

a(n) = 3 iff n is in A023745 but not A000225.

a(n) <= floor(n/2)-1 if n > 9.

Examples

			a(6) = 4 because 6 is 110 in base 2 and 20 in base 3, which do not have nondecreasing digits, but 12 in base 4 has nondecreasing digits.
		

Links

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

Crossrefs

Cf. A000225, A009994, A023745 to A023757.

Programs

Maple

F:= proc(n) local k;
   for k from 2 do if ListTools:-Sorted(convert(n,base,k),`>`) then return k fi od:
end proc:
map(f, [$1..1000]);

Mathematica

Table[k = 2; While[Sort@ # != # &@ IntegerDigits[n, k], k++]; k, {n, 1, 120}] (* Michael De Vlieger, May 14 2016 *)
lk[n_]:=Module[{k=2},While[Min[Differences[IntegerDigits[n,k]]]<0,k++]; k]; Array[lk,90] (* Harvey P. Dale, May 24 2016 *)