A257630 Near-repdigit triangular numbers.

10, 15, 21, 28, 36, 45, 78, 91, 171, 300, 595, 990, 1711, 5565, 6555, 66066, 333336

Offset

1,1

Comments

A near-repdigit is a number having all digits but one equal. No other near-repdigit triangular number is known up to 10^15.

No more terms less than 10^1000. It is likely there are no more terms. - Chai Wah Wu, Mar 25 2020

Links

Table of n, a(n) for n=1..17.

Mathematica

nrepQ[n_] := Module[{dg = Select[DigitCount[n], # > 0 &]}, Length[dg] == 2 && Min[dg] == 1 && Max[dg] > 0]; Select[
Table[n*(n + 1)/2, {n, 10000}], nrepQ]

Prog

(Python)
from sympy import integer_nthroot
def istri(n): return integer_nthroot(8*n+1, 2)[1]
def near_repdigits(digits):
    s = set()
    for d1 in "0123456789":
        for d2 in set("0123456789") - {d1}:
            for loc in range(1, digits+1):
                nrd = d1*(digits-loc) + d2 + d1*(loc-1)
                if nrd[0] != "0": s.add(int(nrd))
    return sorted(s)
def afind(maxdigits):
    for digits in range(2, maxdigits+1):
        for t in near_repdigits(digits):
            if istri(t): print(t, end=", ")
afind(100) # Michael S. Branicky, Oct 15 2021

Crossrefs

Cf. A000217, A010785, A062691.

Sequence in context: A168103 A322045 A062691 * A129496 A075520 A030663

Adjacent sequences: A257627 A257628 A257629 * A257631 A257632 A257633

Keyword

base,nonn,more

Author

Shyam Sunder Gupta, Jul 12 2015

Status

approved