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

0,5

Comments

0 < a(n) <= 10;

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

Links

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

Example

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;

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A080972 A037814 A179529 * A273429 A273915 A270969

Adjacent sequences: A118665 A118666 A118667 * A118669 A118670 A118671

Keyword

nonn,base

Author

Reinhard Zumkeller, May 19 2006

Status

approved