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A045914
Triangular numbers with all digits the same.
15
0, 1, 3, 6, 55, 66, 666
OFFSET
1,3
COMMENTS
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
REFERENCES
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
LINKS
David W. Ballew and Ronald C. Weger, Triangular Numbers with Repeated Digits, Proc. S. D. Acad. Sci., Vol. 51 (1972), pp. 52-55.
David W. Ballew and Ronald C. Weger, Repdigit triangular numbers, J. Rec. Math., Vol. 8, No. 2 (1975-76), pp. 96-98.
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.
FORMULA
A118668(a(n)) = 1. - Reinhard Zumkeller, Jul 11 2015
MATHEMATICA
Select[Union[Flatten[Table[FromDigits[PadRight[{}, n, k]], {n, 3}, {k, 0, 9}]]], OddQ[ Sqrt[8#+1]]&] (* Harvey P. Dale, Feb 11 2020 *)
CROSSREFS
Cf. A213516 (triangular numbers having only 1 or 2 different digits).
Cf. A118668.
Sequence in context: A066569 A051641 A003098 * A370520 A303351 A067610
KEYWORD
fini,full,nonn,base
AUTHOR
EXTENSIONS
0 inserted by T. D. Noe, Jun 22 2012
STATUS
approved