## Benoit Mandelbrot was born on this day 93 years ago.

### Properties of the number 10991:

10991 is a cyclic number.10991 = 29 × 379 is semiprime and squarefree.

10991 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 10584 totatives.

10991 has an oblong digit sum 20 in base 10.

Reversing the decimal digits of 10991 results in an emirpimes.

10991 = 22

^{3}+ 7

^{3}is the sum of 2 positive cubes in 1 way.

10991 = 5496

^{2}- 5495

^{2}= 204

^{2}- 175

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

10991 is the sum of 2 positive triangular numbers.

10991 is the difference of 2 positive pentagonal numbers in 2 ways.

10991 is not the sum of 3 positive squares.

10991

^{2}= 7580

^{2}+ 7959

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

10991

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

10991 is a proper divisor of 1567

^{3}- 1.

10991 is an emirpimes in (at least) the following bases: 2, 4, 8, 10, 11, 15, 17, 18, 19, 20, 22, 25, 27, 31, 32, 41, 43, 46, 47, 49, 54, 61, 65, 67, 68, 74, 76, 77, 80, 81, 82, 84, 85, 87, 90, 91, 97, 99, and 100.

10991 is palindromic in (at least) the following bases: 23, 34, -9, -67, and -99.

10991 in base 4 = 2223233 and consists of only the digits '2' and '3'.

10991 in base 23 = khk and consists of only the digits 'h' and 'k'.

10991 in base 27 = f22 and consists of only the digits '2' and 'f'.

10991 in base 34 = 9h9 and consists of only the digits '9' and 'h'.

10991 in base 60 = 33B and consists of only the digits '3' and 'B'.

### The number 10991 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.A023192: Conjecturally, number of infinitely-recurring prime patterns on n consecutive integers.

A028948: An "extremely strange sequence": a(n+1) = [ A*a(n)+B ]/p^r, where p^r is the highest power of p diving [ A*a(n)+B ] and p=2, A=4.001, B=1.2.

A060354: The n-th n-gonal number.

A066831: Numbers n such that sigma(n) divides sigma(phi(n)).

A067383: Numbers n such that sigma(phi(n))/sigma(n) = 3.

A085366: Semiprimes that are the sum of two positive cubes. Common terms of A003325 and A046315.

A224483: Numbers which are the sum of two positive cubes and divisible by 29.

A252039: T(n,k)=Number of (n+2)X(k+2) 0..4 arrays with every 3X3 subblock row and column sum nonprime and every diagonal and antidiagonal sum prime

A255187: 29-gonal numbers: a(n) = n*(27*n-25)/2.

A262909: a(n) = greatest k such that A155043(k+A262509(n)) < A155043(A262509(n)).