Properties of the Number 21968

Twenty-One Thousand Nine Hundred Sixty-Eight

Basics

Value: 21967 → 21968 → 21969

Parity: even

Prime: No

Previous Prime: 21961

Next Prime: 21977

Digit Sum: 26

Digital Root: 8

Palindrome: No

Factorization: 2 ⁴ × 1373

Divisors: 1, 2, 4, 8, 16, 1373, 2746, 5492, 10984, 21968

Polygonal

Triangular: No

Square: No

Pentagonal: No

Hexagonal: No

Heptagonal: No

Tetrahedral: No

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Representations

Binary: 101010111010000

Octal: 52720

Duodecimal: 10868

Hexadecimal: 55d0

Square: 482593024

Square Root: 148.21605850919124

Classification

Fibonacci: No

Bell Number: No

Factorial Number: No

Regular Number: No

Perfect Number: No

Special

Kaprekar Constant: No

Munchausen Constant: No

Armstrong Number: No

Kaprekar Number: No

Catalan Number: No

Vampire Number: No

Taxicab Number: No

Super Prime: No

Friedman Number: No

Fermat Number: No

Cullen Number: No

OEIS Sequences

Triangle read by rows: T(n,k) is the number of permutations of {1,2,...,n} having k nonincreasing odd cycles (0<=k<=floor(n/3)). A cycle (b(1), b(2), ...) is said to be increasing if, when written with its smallest element in the first position, it satisfies b(1)<b(2)<b(3)<... . A cycle is said to be odd if it has an odd number of entries. For example, the permutation (152)(347)(6)(8) has 1 nonincreasing odd cycle. A186766

Number of distinct circles that can be constructed from an n·n square grid of points using only a compass. A359931

T(n,k)=Number of (n+1)X(k+1) binary arrays with every 2X2 subblock singular. A184686

Number of permutations of {1,2,...,n} having no nonincreasing odd cycles. A cycle (b(1), b(2), ...) is said to be increasing if, when written with its smallest element in the first position, it satisfies b(1)<b(2)<b(3)<... . A cycle is said to be odd if it has an odd number of entries. A186767

Cube root of A030683. A30684

Expansion of ∏_k>=1 ((1 - 4^k*x^k)/(1 + 4^k*x^k))^{1/4^k}. A303490

Number of (n+1) X 4 binary arrays with every 2 X 2 subblock singular. A184680

Number of (n+1) X 5 binary arrays with every 2 X 2 subblock singular. A184681

a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Lucas numbers), t = (odd natural numbers). A24473

Number of length n+3 0..6 arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms. A249705