A year that speaks for itself
----------------------------------
In 1977, Ivan Niven published an article on the numbers that now bear his name and that, like 2020, are divisible by the sum of their digits. In base 10, 2020 is a Niven number ( also called a Harshad number ) because 2 + 0 + 2 + 0 = 4 and 2020 = 4 × 505.
Discover some properties of these integers on the Problems page "Autobiographical numbers".
In 1979, the American architect and designer Buckminster Fuller used the term Scheherazade numbers for palindromic integers (in Synergetics, published by MacMillan), and he could have written 2020 as a self-referential palindrome in base 100. Indeed, 2020 = 20 × 100 + 20 and is therefore written 2020100. In the same spirit, 2020 is a self-descriptive number: it is written using two 0s, zero 1s, two 2s and zero 3s. More generally, John Horton Conway defined look-and-say sequences in 1986 (see the first part of our feature on self-reference, published in our previous issue).
Ease into the new year
----------------------------
