Friday, March 11, 2016

Number of the day: 487

Properties of the number 487:

487 is prime.
487 has 13 antidivisors.
487 has prime digit sum 19 in base 10.
487 is an emirp in (at least) the following bases: 2, 4, 11, 15, 16, 19, 22, 23, 29, 32, 33, 41, 42, 43, 47, 52, 55, 64, 65, 66, 67, 69, 71, 73, 77, 79, 83, 91, 96, 97, and 99.
487 is palindromic in (at least) the following bases: 8, and 18.
487 = 2442 - 2432 is the difference of 2 nonnegative squares in 1 way.
487 is not the sum of 3 positive squares.
487 in base 8 = 747 and consists of only the digits '4' and '7'.
487 in base 15 = 227 and consists of only the digits '2' and '7'.
487 in base 17 = 1bb and consists of only the digits '1' and 'b'.
487 in base 18 = 191 and consists of only the digits '1' and '9'.


The number 487 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A106856: Primes of the form x^2+xy+2y^2, with x and y nonnegative.
A002145: Primes of the form 4n+3.
A002476: Primes of form 6m + 1.
A104272: Ramanujan primes R_n: a(n) is the smallest number such that if x >= a(n), then pi(x) - pi(x/2) >= n, where pi(x) is the number of primes <= x.
A023200: Primes p such that p + 4 is also prime.
A107132: Primes of the form 2x^2+13y^2.
A007510: Single (or isolated or non-twin) primes: Primes p such that neither p-2 nor p+2 is prime.
A007645: Generalized cuban primes: primes of the form x^2 + xy + y^2; or primes of the form x^2 + 3*y^2; or primes == 0 or 1 mod 3.
A065727: Primes p such that the decimal expansion of its base 9 conversion is also prime.
A140633: Primes of the form 7x^2+4xy+52y^2.

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