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A045914
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Triangular numbers with all digits the same.
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15
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OFFSET
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1,3
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COMMENTS
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Escott (1905) proved that there are no more terms with fewer than 30 digits. The complete proof that there are no more terms was given by Ballew and Weger (1972). - Amiram Eldar, Jan 22 2022
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REFERENCES
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L. E. Dickson, History of the Theory of Numbers, Vol. II, p. 33, Chelsea NY, 1952.
E. B. Escott, Math. Quest. Educational Times, New Series, Vol. 8 (1905), pp. 33-34. - N. J. A. Sloane, Mar 31 2014
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LINKS
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Bir Kafle, Florian Luca and Alain Togbé, Triangular Repblocks, Fibonacci Quart., Vol. 56, No. 4 (2018), pp. 325-328.
C. E. Youngman, Problem 15648, Educational Times, Vol. 58, 1905, p. 87; with a solution by E. B. Escott.
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FORMULA
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MATHEMATICA
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Select[Union[Flatten[Table[FromDigits[PadRight[{}, n, k]], {n, 3}, {k, 0, 9}]]], OddQ[ Sqrt[8#+1]]&] (* Harvey P. Dale, Feb 11 2020 *)
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CROSSREFS
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Cf. A213516 (triangular numbers having only 1 or 2 different digits).
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KEYWORD
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fini,full,nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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