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Even numbers usually appear on verso (left-hand) pages, while odd numbers appear on recto (right-hand) pages. In the printing industry, in cases where odd numbers appear on verso pages and even numbers on recto pages, this is referred to as non-traditional folios (in the past, it had been referred to as Chinese folios, however this term has fallen out of favor in recent years).
This means that the algorithm is allowed to terminate in step 4 when p 2 is greater than n. [1] Another refinement is to initially list odd numbers only, (3, 5, ..., n), and count in increments of 2p in step 3, thus marking only odd multiples of p. This actually appears in the original algorithm.
Alternatively, replace the 3n + 1 with n ′ / H(n ′) where n ′ = 3n + 1 and H(n ′) is the highest power of 2 that divides n ′ (with no remainder). The resulting function f maps from odd numbers to odd numbers. Now suppose that for some odd number n, applying this operation k times yields the number 1 (that is, f k (n) = 1).
Even and odd numbers have opposite parities, e.g., 22 (even number) and 13 (odd number) have opposite parities. In particular, the parity of zero is even. [2] Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That ...
This page was last edited on 28 September 2007, at 23:06 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.
Print/export Download as PDF ... Number of odd entries in row n of Pascal's triangle. ... Stella octangula numbers: n(2n 2 − 1), with n ≥ 0. A007588: Types of primes
a highly abundant number has a sum of positive divisors that is greater than any lesser number; that is, σ(n) > σ(m) for every positive integer m < n. Counterintuitively, the first seven highly abundant numbers are not abundant numbers. a prime number has only 1 and itself as divisors; that is, d(n) = 2; a composite number has more than just ...
where n > 1 is an integer and p, q, r are prime numbers, then 2 n × p × q and 2 n × r are a pair of amicable numbers. This formula gives the pairs (220, 284) for n = 2, (17296, 18416) for n = 4, and (9363584, 9437056) for n = 7, but no other such pairs are known. Numbers of the form 3 × 2 n − 1 are known as Thabit numbers.
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