Sunday, January 28, 2018

Number of the day: 9979

Properties of the number 9979:

9979 is a cyclic number.
9979 = 17 × 587 is semiprime and squarefree.
9979 has 2 distinct prime factors, 4 divisors, 7 antidivisors and 9376 totatives.
9979 has a semiprime digit sum 34 in base 10.
9979 has a Fibonacci digit sum 34 in base 10.
Reversing the decimal digits of 9979 results in an emirpimes.
9979 = 49902 - 49892 = 3022 - 2852 is the difference of 2 nonnegative squares in 2 ways.
9979 is the difference of 2 positive pentagonal numbers in 2 ways.
9979 = 32 + 132 + 992 is the sum of 3 positive squares.
99792 = 46962 + 88052 is the sum of 2 positive squares in 1 way.
99792 is the sum of 3 positive squares.
9979 is a proper divisor of 137293 - 1.
9979 = '9' + '979' is the concatenation of 2 semiprime numbers.
9979 is an emirpimes in (at least) the following bases: 9, 10, 13, 14, 15, 17, 19, 20, 21, 22, 23, 24, 37, 40, 41, 42, 43, 44, 49, 50, 52, 54, 57, 63, 64, 65, 67, 68, 70, 72, 73, 75, 78, 82, 87, 88, 89, 91, 96, 97, 98, 99, and 100.
9979 is palindromic in (at least) the following bases: 36, -6, -57, and -58.
9979 in base 6 = 114111 and consists of only the digits '1' and '4'.
9979 consists of only the digits '7' and '9'.
9979 in base 22 = kdd and consists of only the digits 'd' and 'k'.
9979 in base 36 = 7p7 and consists of only the digits '7' and 'p'.
9979 in base 57 = 344 and consists of only the digits '3' and '4'.

The number 9979 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A041020: Numerators of continued fraction convergents to sqrt(14).
A041228: Numerators of continued fraction convergents to sqrt(126).
A042318: Numerators of continued fraction convergents to sqrt(686).
A042709: Denominators of continued fraction convergents to sqrt(884).
A109936: Composite numbers between largest n-digit prime and the smallest (n+1) digit prime.
A178369: Numbers with rounded up arithmetic mean of digits = 9.
A236082: T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the sum of each 2X2 subblock maximum and minimum lexicographically nondecreasing rowwise and columnwise
A266775: Molien series for invariants of finite Coxeter group D_12 (bisected).
A274410: Numbers n such that the Collatz iterations for n and n + 1 have the same length (A078417) but do not meet a certain condition. (See comments.)
A292739: Numbers in which 9 outnumbers all other digits together.

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