Properties of the Number 31501

Thirty-One Thousand Five Hundred One

Basics

Value: 31500 → 31501 → 31502

Parity: odd

Prime: No

Previous Prime: 31489

Next Prime: 31511

Digit Sum: 10

Digital Root: 1

Palindrome: No

Factorization: 17 ² × 109

Divisors: 1, 17, 109, 289, 1853, 31501

Polygonal

Triangular: No

Square: No

Pentagonal: No

Hexagonal: No

Heptagonal: No

Tetrahedral: No

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Representations

Binary: 111101100001101

Octal: 75415

Duodecimal: 16291

Hexadecimal: 7b0d

Square: 992313001

Square Root: 177.48521065147935

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

a(n) = a(n-1) + 2·a(n-2) - a(n-3), with a(0) = a(1) = 0, a(2) = 1. A6053

Number of integer partitions of n whose run-lengths are neither weakly increasing nor weakly decreasing. A332641

Number of (s(0), s(1), ..., s(2n)) such that 0 < s(i) < 7 and |s(i) - s(i-1)| = 1 for i = 1,2,...,2·n, s(0) = 1, s(2n) = 3. A94790

Third row of Pascal-(1,5,1) array A081580. A81589

a(n) = a(n-1) + ∑_k=0..n/3 a(n-3k) with a(0)=1. A113435

Let i be in {1,2,3} and let r >= 0 be an integer. Let p = {p₁, p₂, p₃} = {-2,0,1}, n=2·r+p_i, and define a(-2)=0. Then, a(n)=a(2·r+p_i) gives the quantity of H_7,2,0 tiles in a subdivided H_7,i,r tile after linear scaling by the factor x^r, where x=sqrt(2·cos(π/7)). A187066

Expansion of g.f. (1-2·x+51·x²)/(1-x)³. A257352

Number of partitions p of n such that the number of numbers having multiplicity 1 in p is a part or the number of numbers having multiplicity > 1 is a part. A239737

T(n,k) = Number of n X k arrays containing k copies of 0..n-1 with no element 1 greater than its north or southwest neighbor modulo n and the upper left element equal to 0. A266861

T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with no element 1 greater than its west or northeast neighbor modulo n and the upper left element equal to 0. A266867