A year of digits
\# Alain Zalmanski writes it in the style of Japanese artist Takeshi Kitano, using consecutive digits—as few as possible—and arithmetic symbols:
**2019 = 1 + 2 + (3!) 4 + 5! x 6**
and also: 2019 = 1 + 2345 x 6/7 + 8.
He also writes 2019 as the palindrome 5B5 in base 19.
\# Other members of the editorial team, including François Lavallou, also tried to express 2019 as a sum of consecutive numbers raised to a given power, even if that meant alternating the coefficients:
The sum 1 + 2 + 3 +… does not work, but how about
1 + 2 + 3! + 4 + … + 63, or 1 + 2 – 3 – 4 … – 11 + 12 + 13 + … + 65?
It just goes to show that sometimes one little sign can change everything!
Moving on to higher powers and continuing to adjust the signs, we get:
2019 = 12 – 22 + 32 – 42 – 5 2 + 6 2 +…+ 18 2
2019 = 1 3 – 2 3 – 3 3 + 4 3 – 5 3 + 6 3 – 7 3 + 8 3 + 9 3 + 10 3.
\# Jean-Louis Legrand points out that one can prove without a computer—quite a feat!—that 17 2019 – 16 is a prime number. He adds that the smallest integer n for which 17 *n* – 16 is prime is 11, that 2019 is the sixth such integer, and that beyond that… it remains a mystery!
\# If you want to surprise your friends on social media, send them this "tweet":
π = 3.14159265…337867831652712019…
Admittedly, 2019 occurs in positions 243–246, but, as Mickaël Launay points out, this is the first time in the 21st century that a single "tweet" can list the decimal digits of π until the year’s number appears. Next year, it will take 27 consecutive "tweets", since 2020 does not appear until the 7,285th decimal place!
\# The newsletter of the APMEP’s Strasbourg regional branch reminds us that 2019 is a "happy" number: add the squares of its digits, then repeat… and you will very quickly reach 1.
Two artistic creations --------------------------
\# A romantic poem by Raphaël Douady:
By the magic of the digit seven, O my last one,
The squares of the primes shalt thou sum
The number of the Apocalypse shalt thou find
To ward off the abyss’s dire fate
The digit seven once more shalt thou add
Three times this operation shalt thou repeat
A wonderful year the numbers
wish you!
\# A "magic honeycomb" by mathemagician Dominique Souder, who hopes "that 2019 will be a magical year for everyone in France": add up the numbers surrounding each hexagon!