Collisions of digit sums in bases 2 and 3

Lukas Spiegelhofer

doi:10.1007/s11856-023-2478-8

Collisions of digit sums in bases 2 and 3

Lukas Spiegelhofer

Chair of Mathematics, Statistics and Geometry (380)

Research output: Contribution to journal › Article › Research › peer-review

Abstract

We prove a folklore conjecture concerning the sum-of-digits functions in bases two and three: there are infinitely many positive integers n such that the sum of the binary digits of n equals the sum of the ternary digits of n.

Original language	English
Pages (from-to)	475–502
Number of pages	28
Journal	Israel journal of mathematics
Volume	258.2023
Issue number	December
DOIs	https://doi.org/10.1007/s11856-023-2478-8
Publication status	Published - 13 Mar 2023

Keywords

sum-of-digits function
digital expansions in different bases

Access to Document

10.1007/s11856-023-2478-8

Cite this

@article{ab2a1c9d65b34f838fdf19e3414f9d37,

title = "Collisions of digit sums in bases 2 and 3",

abstract = "We prove a folklore conjecture concerning the sum-of-digits functions in bases two and three: there are infinitely many positive integers n such that the sum of the binary digits of n equals the sum of the ternary digits of n. ",

keywords = "sum-of-digits function, digital expansions in different bases",

author = "Lukas Spiegelhofer",

year = "2023",

month = mar,

day = "13",

doi = "10.1007/s11856-023-2478-8",

language = "English",

volume = "258.2023",

pages = "475–502",

journal = "Israel journal of mathematics",

issn = "0021-2172",

publisher = "Springer New York",

number = "December",

}

TY - JOUR

T1 - Collisions of digit sums in bases 2 and 3

AU - Spiegelhofer, Lukas

PY - 2023/3/13

Y1 - 2023/3/13

N2 - We prove a folklore conjecture concerning the sum-of-digits functions in bases two and three: there are infinitely many positive integers n such that the sum of the binary digits of n equals the sum of the ternary digits of n.

AB - We prove a folklore conjecture concerning the sum-of-digits functions in bases two and three: there are infinitely many positive integers n such that the sum of the binary digits of n equals the sum of the ternary digits of n.

KW - sum-of-digits function

KW - digital expansions in different bases

UR - https://link.springer.com/article/10.1007/s11856-023-2478-8

U2 - 10.1007/s11856-023-2478-8

DO - 10.1007/s11856-023-2478-8

M3 - Article

SN - 0021-2172

VL - 258.2023

SP - 475

EP - 502

JO - Israel journal of mathematics

JF - Israel journal of mathematics

IS - December

ER -

Collisions of digit sums in bases 2 and 3

Abstract

Keywords

Access to Document

Other files and links

Cite this