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A257630 Near-repdigit triangular numbers.

%I A257630 #23 Oct 15 2021 06:05:47
%S A257630 10,15,21,28,36,45,78,91,171,300,595,990,1711,5565,6555,66066,333336
%N A257630 Near-repdigit triangular numbers.
%C A257630 A near-repdigit is a number having all digits but one equal. No other near-repdigit triangular number is known up to 10^15.
%C A257630 No more terms less than 10^1000. It is likely there are no more terms. - _Chai Wah Wu_, Mar 25 2020
%t A257630 nrepQ[n_] := Module[{dg = Select[DigitCount[n], # > 0 &]},Length[dg] == 2 && Min[dg] == 1 && Max[dg] > 0]; Select[
%t A257630 Table[n*(n + 1)/2, {n, 10000}], nrepQ]
%o A257630 (Python)
%o A257630 from sympy import integer_nthroot
%o A257630 def istri(n): return integer_nthroot(8*n+1, 2)[1]
%o A257630 def near_repdigits(digits):
%o A257630     s = set()
%o A257630     for d1 in "0123456789":
%o A257630         for d2 in set("0123456789") - {d1}:
%o A257630             for loc in range(1, digits+1):
%o A257630                 nrd = d1*(digits-loc) + d2 + d1*(loc-1)
%o A257630                 if nrd[0] != "0": s.add(int(nrd))
%o A257630     return sorted(s)
%o A257630 def afind(maxdigits):
%o A257630     for digits in range(2, maxdigits+1):
%o A257630         for t in near_repdigits(digits):
%o A257630             if istri(t): print(t, end=", ")
%o A257630 afind(100) # _Michael S. Branicky_, Oct 15 2021
%Y A257630 Cf. A000217, A010785, A062691.
%K A257630 base,nonn,more
%O A257630 1,1
%A A257630 _Shyam Sunder Gupta_, Jul 12 2015