cp's OEIS Frontend

By definition, a(n) is the degree of the minimal polynomial of sin(n degrees).

Periodic sequence of period 360.

The sequence range is the set of all divisors of 48 (A018261), where 48 = Euler_phi(180) = A000010(180).

All 48 distinct algebraic numbers of degree 48 referenced here (i.e., where GCD(n, 180) = 1) have the same minimal polynomial, which is shown in A019810.

Students who are first learning about prime and composite numbers and factorization learn that trial division is a simple way to determine whether a given number N is prime, and that only those divisors up through the square root of N need to be tried, since trial division by each prime up through a given prime p is sufficient to completely factor every composite number up through at least p^2.

Given a four-function calculator and a set of randomly-selected integers of manageable size to either factor or identify as prime, one can observe fairly quickly that as trial division is attempted using the primes in increasing order as divisors, many numbers that aren't divisible by any of the first several primes turn out to be prime.

Given some positive integer j > prime(n)^2, if we consider the set of integers that exceed prime(n)^2 but do not exceed j, and we exclude each number that is divisible by any of the first n primes, then the numbers that remain will include exactly as many primes as composites if j = a(n), but if j < a(n), then most of the numbers that remain will be prime.