GOTW- Counting - Page 14

110 is a sphenic number and a pronic number. Following the prime quadruplet (101, 103, 107, 109), at 110, the Mertens function reaches a low of -5.

110 is the sum of three consecutive squares, .

110 is the side of the smallest square that can be tiled with distinct integer-sided squares.

RSA-110 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge.

The Rule 110 cellular automaton, like Conway's Game of Life, exhibits what Stephen Wolfram calls "Class 4 behavior," which is neither completely random nor completely repetitive.^[1]

An example run of a rule 110 cellular automaton

In base 10, the number 110 is a Harshad number and a self number.

😆 😆

111 is a perfect totient number.

111 is R₃ or the second repunit, a number like 11, 111, or 1111 that consists of repeated units, or 1's. It equals 3 37, therefore all triplets (numbers like222 or 777) in base ten are of the form 3n 37.

All triplets in all bases are multiples of 111 in that base, therefore the number represented by 111 in a particular base is the only triplet that can ever be prime. 111 is not prime in base ten, but is prime in base two, where 111₂ = 7₁₀. It is also prime in these other bases up to 100: 3, 5, 6, 8, 12, 14, 15, 17, 20, 21, 24, 27, 33, 38, 41, 50, 54, 57, 59, 62, 66, 69, 71, 75, 77, 78, 80, 89, 90, and 99. 111 is also prime in base 111 (= 12433₁₀).

In radix 18 the number 111 is the third power of seven 7³ (= 343₁₀) which is the only radix where 111 is a power.

The smallest magic square using only 1 and prime numbers has a magic constant of 111:

Originally posted by: -Nakshatra-

We posted in the same time but you made a mistake and edited it.. Whose fault is it 😡

She posted 107 and i posted 108 😡

One hundred [and] twelve is an abundant number and aheptagonal number. It is also the sum of six consecutiveprimes ().

112 is in base 10 both a Harshad number.

Yeh den i realised Lik did 107! so i edited before u posted 😆 easy mistake.