Saturday, May 12, 2018

Number of the day: 9121

Properties of the number 9121:

9121 = 7 × 1303 is semiprime and squarefree.
9121 has 2 distinct prime factors, 4 divisors, 13 antidivisors and 7812 totatives.
9121 has an emirp digit sum 13 in base 10.
9121 has a Fibonacci digit sum 13 in base 10.
Reversing the decimal digits of 9121 results in an emirpimes.
9121 = 45612 - 45602 = 6552 - 6482 is the difference of 2 nonnegative squares in 2 ways.
9121 is the sum of 2 positive triangular numbers.
9121 is the difference of 2 positive pentagonal numbers in 2 ways.
9121 = 112 + 302 + 902 is the sum of 3 positive squares.
91212 is the sum of 3 positive squares.
9121 is a proper divisor of 13996 - 1.
9121 = '9' + '121' is the concatenation of 2 semiprime numbers.
9121 = '91' + '21' is the concatenation of 2 triangular numbers.
9121 is an emirpimes in (at least) the following bases: 2, 3, 4, 10, 13, 15, 18, 20, 21, 23, 26, 31, 37, 38, 41, 43, 45, 47, 49, 54, 56, 57, 59, 63, 65, 66, 67, 68, 69, 72, 75, 77, 79, 81, 84, 85, 88, 89, 90, 94, 98, 99, and 100.
9121 is palindromic in (at least) the following bases: 76, 80, 95, -43, and -96.
9121 in base 22 = iid and consists of only the digits 'd' and 'i'.
9121 in base 25 = eel and consists of only the digits 'e' and 'l'.
9121 in base 42 = 577 and consists of only the digits '5' and '7'.

The number 9121 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000993: Number of distinct quadratic residues mod 10^n; also number of distinct n-digit endings of base-10 squares.
A064843: A064842/2.
A106734: a(n) = n^3 - 7*n + 7.
A176069: Products of two distinct primes of the form n^2+n+1.
A195158: Concentric 24-gonal numbers.
A216097: 3^n mod 10000.
A228219: Number of second differences of arrays of length 4 of numbers in 0..n.
A256101: The broken eggs problem.
A259184: a(n) = 1 - sigma(n) + sigma(n)^2.
A272039: a(n) = 10*n^2 + 4*n + 1.

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