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Near-repdigit triangular numbers.
1

%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