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Example: as shown in the following figure of Floyd's triangle, 25 is a centered square number, and is the sum of the square 16 (yellow rhombus formed by shearing a square) and of the next smaller square, 9 (sum of two blue triangles): Centered square numbers (in red) are in the center of odd rows of Floyd's triangle.
Here, the list [0..] represents , x^2>3 represents the predicate, and 2*x represents the output expression.. List comprehensions give results in a defined order (unlike the members of sets); and list comprehensions may generate the members of a list in order, rather than produce the entirety of the list thus allowing, for example, the previous Haskell definition of the members of an infinite list.
which is both the t-th triangular number and the s-th square number. A near-isosceles Pythagorean triple is an integer solution to a 2 + b 2 = c 2 where a + 1 = b. The next table shows that splitting the odd number H n into nearly equal halves gives a square triangular number when n is even and a near isosceles Pythagorean triple when n is odd ...
The examples below implement the perfect digital invariant function for = and a default base = described in the definition of happy given at the top of this article, repeatedly; after each time, they check for both halt conditions: reaching 1, and repeating a number. A simple test in Python to check if a number is happy:
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
Introduced in Python 2.2 as an optional feature and finalized in version 2.3, generators are Python's mechanism for lazy evaluation of a function that would otherwise return a space-prohibitive or computationally intensive list. This is an example to lazily generate the prime numbers:
Payouts are based on the last digit of the score of each team at the end of the first quarter, half, third quarter, and game. ... The numbers are based on a $50 a square game, with a $625 payout ...
1624 = number of squares in the Aztec diamond of order 28 [366] 1625 = centered square number [14] 1626 = centered pentagonal number [46] 1627 = prime and 2 × 1627 - 1 = 3253 is also prime [367] 1628 = centered pentagonal number [46] 1629 = rounded volume of a regular tetrahedron with edge length 24 [289] 1630 = number k such that k^64 + 1 is ...