### Properties of the number 337:

337 is the 68^{th}prime.

337 has 11 antidivisors and 336 totatives.

337 has an emirp digit sum 13 in base 10.

337 has a Fibonacci digit sum 13 in base 10.

Reversing the decimal digits of 337 results in an emirp.

337 = 169

^{2}- 168

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

337 is the difference of 2 positive pentagonal numbers in 1 way.

337 = 9

^{2}+ 16

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

337 = 2

^{2}+ 3

^{2}+ 18

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

337

^{2}= 175

^{2}+ 288

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

337

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

337 is a divisor of 673

^{2}- 1.

337 = '3' + '37' is the concatenation of 2 prime numbers.

337 is an emirp in (at least) the following bases: 2, 4, 5, 6, 7, 10, 11, 19, 21, 23, 25, 33, 34, 37, 39, 44, 45, 47, 49, 53, 57, 58, 64, 66, 67, 71, 77, 79, 83, 88, 91, 95, and 98.

337 is palindromic in (at least) the following bases: 9, 14, 16, -21, -24, -28, -42, -48, -56, and -84.

337 in base 3 = 110111 and consists of only the digits '0' and '1'.

337 in base 4 = 11101 and consists of only the digits '0' and '1'.

337 in base 5 = 2322 and consists of only the digits '2' and '3'.

337 in base 7 = 661 and consists of only the digits '1' and '6'.

337 in base 9 = 414 and consists of only the digits '1' and '4'.

337 consists of only the digits '3' and '7'.

337 in base 13 = 1cc and consists of only the digits '1' and 'c'.

337 in base 14 = 1a1 and consists of only the digits '1' and 'a'.

337 in base 15 = 177 and consists of only the digits '1' and '7'.

337 in base 16 = 151 and consists of only the digits '1' and '5'.

### The number 337 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.A000695: Moser-de Bruijn sequence: sums of distinct powers of 4.

A002144: Pythagorean primes: primes of form 4n + 1.

A002313: Primes congruent to 1 or 2 modulo 4; or, primes of form x^2+y^2; or, -1 is a square mod p.

A002476: Primes of form 6m + 1.

A005836: Numbers n whose base 3 representation contains no 2.

A006567: Emirps (primes whose reversal is a different prime).

A029495: Numbers n such that n divides the (right) concatenation of all numbers <= n written in base 2 (most significant digit on right).

A068228: Primes congruent to 1 (mod 12).

A106856: Primes of the form x^2+xy+2y^2, with x and y nonnegative.

A211422: Number of ordered triples (w,x,y) with all terms in {-n,...,0,...,n} and w^2+x*y=0.

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