## Happy New Year!

### Properties of the number 2017:

2017 is the 306

^{th} prime.

2017 has 9

antidivisors and 2016

totatives.

2017 has a

semiprime digit sum 10 in base 10.

2017 has a

triangular digit sum 10 in base 10.

2017 has sum of divisors equal to 2018 which is an

emirpimes.

Reversing the decimal digits of 2017 results in a

sphenic number.

2017 = 1009

^{2} - 1008

^{2} is the difference of 2 nonnegative squares in 1 way.

2017 is the sum of 2 positive

triangular numbers.

2017 is the difference of 2 positive

pentagonal numbers in 1 way.

2017 = 9

^{2} + 44

^{2} is the sum of 2 positive squares in 1 way.

2017 = 21

^{2} + 26

^{2} + 30

^{2} is the sum of 3 positive squares.

2017

^{2} = 792

^{2} + 1855

^{2} is the sum of 2 positive squares in 1 way.

2017

^{2} is the sum of 3 positive squares.

2017 is a divisor of 229

^{4} - 1.

2017 is an

emirp in (at least) the following bases: 2, 3, 4, 7, 8, 9, 12, 16, 17, 19, 25, 33, 34, 37, 38, 45, 47, 49, 53, 54, 57, 59, 61, 64, 67, 68, 71, 74, 75, 77, 79, 83, 89, 92, 95, and 97.

2017 is

palindromic in (at least) the following bases: 31, 32, 36, 42, -8, -48, -56, -63, -72, -84, and -96.

2017 in base 30 = 277 and consists of only the digits '2' and '7'.

2017 in base 31 = 232 and consists of only the digits '2' and '3'.

2017 in base 32 = 1v1 and consists of only the digits '1' and 'v'.

2017 in base 35 = 1mm and consists of only the digits '1' and 'm'.

2017 in base 36 = 1k1 and consists of only the digits '1' and 'k'.

2017 in base 41 = 188 and consists of only the digits '1' and '8'.

2017 in base 42 = 161 and consists of only the digits '1' and '6'.

2017 in base 44 = 11b and consists of only the digits '1' and 'b'.

Sequence numbers and descriptions below are taken from

OEIS.

A005108: Class 4+ primes (for definition see

A005105).

A005383: Numbers n such that both n and (n+1)/2 are primes.

A028916: Friedlander-Iwaniec primes: Primes of form a^2 + b^4.

A033215: Primes of form x^2+21*y^2.

A049774: Number of permutations of n elements not containing the consecutive pattern 123.

A107008: Primes of the form x^2+24*y^2.

A142006: Primes congruent to 2 mod 31.

A212959: Number of (w,x,y) such that w,x,y are all in {0,...,n} and |w-x|=|x-y|.

A235394: Primes whose decimal representation is a valid number in base 8 and interpreted as such is again a prime.

A242784: Number A(n,k) of permutations of [n] avoiding the consecutive step pattern given by the binary expansion of k, where 1=up and 0=down; square array A(n,k), n>=0, k>=0, read by antidiagonals.