Properties of the Number 63697

Sixty-Three Thousand Six Hundred Ninety-Seven

Basics

Value: 63696 → 63697 → 63698

Parity: odd

Prime: Yes

Previous Prime: 63691

Next Prime: 63703

Digit Sum: 31

Digital Root: 4

Palindrome: No

Factorization: 63697

Divisors: 1, 63697

Polygonal

Triangular: No

Square: No

Pentagonal: No

Hexagonal: No

Heptagonal: No

Tetrahedral: No

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Representations

Binary: 1111100011010001

Octal: 174321

Duodecimal: 30A41

Hexadecimal: f8d1

Square: 4057307809

Square Root: 252.3826459961144

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

The O(1) loop model on the square lattice is defined as follows: At every vertex the loop turns to the left or to the right with equal probability, unless the vertex has been visited before, in which case the loop leaves the vertex via the unused edge. Every vertex is visited twice. The probability that a face of the lattice on an n X infinity cylinder is surrounded by one loop is conjectured to be given by a(n)/A_HT(n)², where A_HT(n) is the number of n X n half turn symmetric alternating sign matrices. A92373

T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero. A299893

Balanced primes (A090403) of index 4. A96708

Second term of balanced prime quartets: p(m)-p(m-1) = p(m+1)-p(m) = p(m+2)-p(m+1). A54801

Numbers k such that k and k+6 are both balanced primes. A173892

Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..6 array extended with zeros and convolved with 1,1. A222332

Number of 6Xn -1,1 arrays such that the sum over i=1..6,j=1..n of i·x(i,j) is zero, the sum of x(i,j) is zero, and rows are nondecreasing (number of ways to distribute n-across galley oarsmen left-right at 6 fore-aft positions so that there are no turning moments on the ship). A225346

Number of n X 3 0..1 arrays with every element equal to 0, 2, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero. A299888

Number of walks within N³ (the first octant of Z³) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, -1, 1), (-1, 1, -1), (0, 0, 1), (1, 0, -1)}. A148004

Positions of positive coefficients in cyclotomic polynomial Phi_n(x), A063696 in binary. A63697