A234848 Triangular numbers with digits in nondecreasing order.

0, 1, 3, 6, 15, 28, 36, 45, 55, 66, 78, 136, 378, 666, 1128, 1225, 1378, 2278, 2346, 2556, 5778, 12246, 13366, 22366, 22578, 35778, 111156, 222778, 223446, 333336, 1113778, 1222266, 1457778, 2235555, 3557778, 22227778, 22234446, 111116778, 156777778, 222446778

Offset: 1

Author

Zak Seidov, Dec 31 2013

Keywords

• base
• nonn

Comments

Beyond 222446778, all terms are k(k+1)/2 for k = 2s7, 6s7, or 6s8, where s stands for any number of 6's. - T. D. Noe, Jan 01 2014

Links

• T. D. Noe, Table of n, a(n) for n = 1..328 (terms less than 10^200)

Crossrefs

Cf. A000217, A028820.

Programs

Mathematica

inOrder[nums_] := Min[Differences[nums]] >= 0; t = {}; Do[tri = n*(n+1)/2; If[inOrder[IntegerDigits[tri]], AppendTo[t, tri]], {n, 0, 10^5}]; t (* T. D. Noe, Dec 31 2013 *)
Select[Accumulate[Range[0,22000]],Min[Differences[IntegerDigits[#]]]>=0&] (* Harvey P. Dale, Apr 06 2023 *)

Python

from itertools import chain, count, islice, combinations_with_replacement
from sympy import integer_nthroot
def A234848_gen(): # generator of terms
    return chain((0,), (n for n in (int(''.join(i)) for l in count(1) for i in combinations_with_replacement('123456789',l)) if integer_nthroot(8*n+1,2)[1]))
A234848_list = list(islice(A234848_gen(),50)) # Chai Wah Wu, May 22 2022