### Properties of the number 1337:

1337 = 7 × 191 is semiprime and squarefree.1337 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 1140 totatives.

1337 has a semiprime digit sum 14 in base 10.

Reversing the decimal digits of 1337 results in a prime.

1337 = 669

^{2}- 668

^{2}= 99

^{2}- 92

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

1337 is the difference of 2 positive pentagonal numbers in 2 ways.

1337 = 4

^{2}+ 5

^{2}+ 36

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

1337

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

1337 is a divisor of 421

^{5}- 1.

1337 = '13' + '37' is the concatenation of 2 emirps.

1337 is an emirpimes in (at least) the following bases: 2, 5, 7, 9, 17, 23, 27, 28, 29, 30, 37, 38, 40, 41, 42, 43, 44, 45, 49, 55, 59, 60, 61, 62, 66, 67, 71, 75, 76, 77, 81, 82, 83, 84, 91, 93, 95, 96, 98, 99, and 100.

1337 is palindromic in (at least) the following bases: -14, -18, and -23.

1337 in base 3 = 1211112 and consists of only the digits '1' and '2'.

1337 in base 13 = 7bb and consists of only the digits '7' and 'b'.

1337 in base 36 = 115 and consists of only the digits '1' and '5'.

### The number 1337 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.A033681: a(1) = 3; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

A075928: List of codewords in binary lexicode with Hamming distance 4 written as decimal numbers.

A084600: Triangle, read by rows, where the n-th row lists the (2n+1) coefficients of (1+x+2x^2)^n for n>=0.

A121027: Multiples of 7 containing a 7 in their decimal representation.

A162527: Numbers n such that their largest divisor <= sqrt(n) equals 7.

A191450: Dispersion of (3n-1), read by antidiagonals.

A239405: T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of the elements above it, modulo 4

A254051: Square array A by downward antidiagonals: A(n,k) = (3 + 3^n*(2*floor(3*k/2) - 1))/6, n,k >= 1; read as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

A254100: Postludic numbers: Second column of Ludic array A255127.

A256082: Non-palindromic balanced numbers in base 2.

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