Properties of the Number -163

One Hundred Sixty-Three

Basics

Value: -164 → -163 → -162

Parity: odd

Prime: No

Previous Prime:

Next Prime: 1

Digit Sum: 10

Digital Root: 1

Palindrome: No

Factorization: 163

Divisors: 1, 163

Polygonal

Triangular: No

Square: No

Pentagonal: No

Hexagonal: No

Heptagonal: No

Tetrahedral: No

Today's Target

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Representations

Binary: -10100011

Octal: -243

Duodecimal: -117

Hexadecimal: -a3

Square: 26569

Square Root: 12.767145334803704

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) = (-n³ + 9n² - 5n + 3)/3. A161702

Dirichlet inverse of A129283, n + A003415(n). A347084

Signed primes: if prime(n) even, a(n) = 0; if prime(n) == 1 (mod 4), a(n) = prime(n); if prime(n) == -1 (mod 4), a(n) = -prime(n). A73579

Expansion of 1/(1 - x + x⁴). A99530

G.f. satisfies: A(x) = 1/(1 + x·A(x⁴)) and also the continued fraction: 1 + x·A(x⁵) = [1; 1/x, 1/x⁴, 1/x¹⁶, 1/x⁶⁴, ..., 1/x^{4^(n-1}), ...]. A101914

a(n) = 36·n² - 810·n + 2753, producing the conjectured record number of 45 primes in a contiguous range of n for quadratic polynomials, i.e., abs(a(n)) is prime for 0 <= n < 44. A117081

Expansion of q* (ψ(q⁹)/φ(q⁹))/ (ψ(q)/φ(q)) in powers of q where ψ(),φ() are Ramanujan θ functions. A128143

Coefficients of the '10th-order' mock θ function χ(q). A53284

Simple quadratic fields (i.e., with a unique prime factorization). A61574

Expansion of ψ(q³)* φ(-q³)* χ²(-q³)/( ψ(-q)* φ(-q¹⁸)) in powers of q where φ(), ψ(), χ() are Ramanujan θ functions. A128145