A255678 -id:A255678 - cp's OEIS frontend

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

Reinhard Zumkeller, May 19 2006

0 < a(n) <= 10;

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

			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;

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

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

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

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

A260214 a(n) is the first triangular number whose decimal representation uses n distinct digits.

Original entry on oeis.org

0, 10, 105, 1035, 10296, 102378, 1024596, 10348975, 102738945, 1062489753

Offset: 1

Anders Hellström, Jul 19 2015

Anders Hellström, Table of n, a(n) for n = 1..10

Cf. A000217, A043537, A118668, A255678.

# (# + 1)/2 & /@ {0, 4, 14, 45, 143, 452, 1431, 4549, 14334, 46097} (* terms in A255678 *) (* Robert G. Wilson v, Jul 21 2015 *)

number_of_distinct_digits(m) = if(m==0,1,#vecsort(digits(m), , 8))
a(n)=my(m=0); while(!(number_of_distinct_digits(m*(m+1)/2)==n), m++); m*(m+1)/2;
first(m)=vector(m, n, a(n)) \\m<=10 /* Anders Hellström, Aug 03 2015 */

a(n) = A255678(n)*(A255678(n)+1)/2.

cp's OEIS Frontend

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

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