Properties of the Number 10405

Ten Thousand Four Hundred Five

Basics

Value: 10404 → 10405 → 10406

Parity: odd

Prime: No

Previous Prime: 10399

Next Prime: 10427

Digit Sum: 10

Digital Root: 1

Palindrome: No

Factorization: 5 × 2081

Divisors: 1, 5, 2081, 10405

Polygonal

Triangular: No

Square: No

Pentagonal: No

Hexagonal: No

Heptagonal: No

Tetrahedral: No

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Representations

Binary: 10100010100101

Octal: 24245

Duodecimal: 6031

Hexadecimal: 28a5

Square: 108264025

Square Root: 102.00490184299969

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

T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4. A240000

a(n) is smallest natural number a satisfying Pell equation a² - d(n)*b²= +1 or = -1, with d(n)=A000037(n) (a nonsquare). Corresponding smallest b(n)=A077233(n). A77232

Number of partitions p = [x(1), ..., x(k)], where x(1) >= x(2) >= ... >= x(k), of n such that max(x(i) - x(i-1)) > number of parts of p. A241832

O.g.f. A(x) satisfies: A(x) = x * (1 - 4·x*A'(x)) / (1 - 5·x*A'(x)). A300991

a(n) = 9·n² + 1. A247792

Numbers k such that prime(k+3)-(k+3)*τ(k+3) = prime(k-3)-(k-3)*τ(k-3) where τ(k) = A000005(k) is the number of divisors of k. A67355

a(n) = 36·n² + 1. A158591

Average of squares of successive primes: a(n) = (prime(n+1)² + prime(n)²)/2, with n >= 2. A75892

Numerators of continued fraction convergents to sqrt(774). A42492

a(n) = 14641·n² - 24684·n + 10405. A157442