Number of the day: 1663

Henri Poincaré was born on this day 164 years ago.

Properties of the number 1663:

1663 is a cyclic number.
1663 is the 261^th prime.
1663 has 13 antidivisors and 1662 totatives.
Reversing the decimal digits of 1663 results in a semiprime.
1663 = 832² - 831² is the difference of 2 nonnegative squares in 1 way.
1663 is the sum of 2 positive triangular numbers.
1663 is the difference of 2 positive pentagonal numbers in 1 way.
1663 is not the sum of 3 positive squares.
1663² is the sum of 3 positive squares.
1663 is a proper divisor of 41²⁷⁷ - 1.
1663 is an emirp in (at least) the following bases: 4, 12, 18, 19, 25, 30, 32, 34, 36, 41, 47, 49, 50, 51, 52, 53, 56, 57, 59, 63, 64, 66, 67, 70, 71, 75, 76, 79, 83, 84, 85, 91, and 93.
1663 is palindromic in (at least) the following bases: 6, and -21.
1663 in base 6 = 11411 and consists of only the digits '1' and '4'.
1663 in base 20 = 433 and consists of only the digits '3' and '4'.
1663 in base 23 = 337 and consists of only the digits '3' and '7'.
1663 in base 40 = 11N and consists of only the digits '1' and 'N'.

The number 1663 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A007529: Prime triples: n; n+2 or n+4; n+6 all prime.
A007658: Numbers n such that (3^n + 1)/4 is prime.
A007690: Number of partitions of n in which no part occurs just once.
A022005: Initial members of prime triples (p, p+4, p+6).
A059802: Numbers n such that 5^n - 4^n is prime.
A127576: Primes of the form 16n+15.
A140633: Primes of the form 7x^2+4xy+52y^2.
A161206: V-toothpick (or honeycomb) sequence (see Comments lines for definition).
A187220: Gullwing sequence (see Comments lines for precise definition).
A235394: Primes whose decimal representation is a valid number in base 8 and interpreted as such is again a prime.