Friday, January 1, 2021

Number of the day: 2021

Happy New Year!

Properties of the number 2021:

2021 is a cyclic number.
2021 = 43 × 47 is semiprime and squarefree.
2021 has 2 distinct prime factors, 4 divisors, 9 antidivisors and 1932 totatives.
2021 has a prime digit sum 5 in base 10.
2021 has a Fibonacci digit sum 5 in base 10.
Reversing the decimal digits of 2021 results in an emirpimes.
2021 = 10112 - 10102 = 452 - 22 is the difference of 2 nonnegative squares in 2 ways.
2021 is the difference of 2 positive pentagonal numbers in 1 way.
2021 = 12 + 162 + 422 is the sum of 3 positive squares.
20212 is the sum of 3 positive squares.
2021 is a proper divisor of 10332 - 1.
2021 is an emirpimes in (at least) the following bases: 2, 4, 5, 10, 12, 14, 17, 21, 23, 25, 27, 29, 33, 36, 38, 39, 42, 44, 49, 51, 55, 57, 62, 67, 76, 81, 85, 86, 87, 89, 91, 94, 95, 96, and 98.
2021 is palindromic in (at least) the following bases: 46, -10, and -21.
2021 in base 20 = 511 and consists of only the digits '1' and '5'.
2021 in base 44 = 11f and consists of only the digits '1' and 'f'.

The number 2021 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001704: a(n) = n concatenated with n + 1.
A006094: Products of 2 successive primes.
A028347: a(n) = n^2 - 4.
A052219: Numbers whose sum of digits is 5.
A061037: Numerator of 1/4 - 1/n^2.
A078371: a(n) = (2*n+5)*(2*n+1).
A202018: a(n) = n^2 + n + 41.
A299258: Coordination sequence for 3D uniform tiling formed by stacking parallel layers of the 4.6.12 2D tiling (cf. A072154).
A299276: Partial sums of A008137.
A326256: MM-numbers of nesting multiset partitions.

No comments:

Post a Comment