A118668 Number of distinct digits needed to write the n-th triangular number in decimal representation.

1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 1, 3, 3, 3, 3, 3, 3, 3, 2, 4, 3, 3, 3, 3, 4, 4, 4, 3, 4, 4, 4, 4, 2, 3, 4, 3, 4, 4, 3, 4, 2, 3, 4, 4, 4, 3, 3, 4, 3, 4, 3, 2, 4, 4, 4, 3, 3, 4, 4, 3, 4, 3, 4, 3, 4, 4, 4, 4, 3, 4, 3, 4, 4, 4, 2, 2, 3, 3, 4

Offset: 0

Author

Reinhard Zumkeller, May 19 2006

Keywords

• nonn
• base

Comments

0 < a(n) <= 10;

a(n) = A043537(A000217(n)).

Examples

			n=99: 99*(99+1)/2 = 4950 -> a(99) = #{0,4,5,9} = 4;
see A119033 for an overview of sequences with terms composed of not more than 3 distinct digits.
n=100: 100*(100+1)/2 = 5050 -> a(100) = #{0,5} = 2;
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000217, A043537, A045914, A213517, A213518, A255678.

Programs

Haskell

a118668 = a043537 . a000217
a118668_list = map a043537 a000217_list
-- Reinhard Zumkeller, Jul 11 2015

Mathematica

Length[Union[IntegerDigits[#]]]&/@Accumulate[Range[0,110]] (* Harvey P. Dale, Jul 23 2012 *)