Friday, September 4, 2020

Number of the day: 95101

Properties of the number 95101:

95101 is a cyclic number.
95101 is the 9168th prime.
95101 has 9 antidivisors and 95100 totatives.
95101 has sum of divisors equal to 95102 which is a sphenic number.
Reversing the decimal digits of 95101 results in an emirp.
95101 = 475512 - 475502 is the difference of 2 nonnegative squares in 1 way.
95101 is the sum of 2 positive triangular numbers.
95101 is the difference of 2 positive pentagonal numbers in 1 way.
95101 = 1492 + 2702 is the sum of 2 positive squares in 1 way.
95101 = 502 + 512 + 3002 is the sum of 3 positive squares.
951012 = 506992 + 804602 is the sum of 2 positive squares in 1 way.
951012 is the sum of 3 positive squares.
95101 is a proper divisor of 733300 - 1.
95101 is an emirp in (at least) the following bases: 9, 10, 11, 15, 21, 23, 25, 26, 29, 35, 42, 43, 45, 49, 52, 55, 59, 67, 70, 85, and 92.
95101 is palindromic in (at least) the following bases: 69, 84, and -51.
95101 in base 48 = fDD and consists of only the digits 'D' and 'f'.

The number 95101 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A032629: Primes that are concatenations of n with n + 6.
A105010: Primes from merging of 5 successive digits in decimal expansion of exp(Pi).
A154822: Primes p of the form : p+p^2+p^3-+4=prime.
A167626: Prime numbers ending in the prime number 101.
A179037: Emirps with a 5 as the only prime digit.
A183546: Number of n X n 0..2 arrays with each element equal to either the maximum or the minimum of its horizontal and vertical neighbors
A183549: Number of nX4 0..2 arrays with each element equal to either the maximum or the minimum of its horizontal and vertical neighbors
A183554: T(n,k)=Number of nXk 0..2 arrays with each element equal to either the maximum or the minimum of its horizontal and vertical neighbors

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