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