login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A045914 Triangular numbers with all digits the same. 15
0, 1, 3, 6, 55, 66, 666 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Escott (1905) proved that there are no more terms with less 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 * A303351 A067610 A067609

Adjacent sequences:  A045911 A045912 A045913 * A045915 A045916 A045917

KEYWORD

fini,full,nonn,base

AUTHOR

Felice Russo

EXTENSIONS

Added 0 - T. D. Noe, Jun 22 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 4 11:02 EDT 2022. Contains 355075 sequences. (Running on oeis4.)