A045914 Triangular numbers with all digits the same.

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

Table of n, a(n) for n=1..7.

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

Adjacent sequences: A045911 A045912 A045913 * A045915 A045916 A045917

Keyword

fini,full,nonn,base

Author

Felice Russo

Extensions

0 inserted by T. D. Noe, Jun 22 2012

Status

approved