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

1,3

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)

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 *)

Prog

(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

Crossrefs

Cf. A000217, A028820.

Sequence in context: A000740 A056278 A161625 * A300761 A069712 A076971

Adjacent sequences: A234845 A234846 A234847 * A234849 A234850 A234851

Keyword

base,nonn

Author

Zak Seidov, Dec 31 2013

Status

approved