Pernicious number

In number theory, a pernicious number is a positive integer where the Hamming weight (or digit sum) of its binary representation is prime.

Examples

The first pernicious number is 3, since 3 = 11₂ and 1 + 1 = 2, which is a prime. The next pernicious number is 5, since 5 = 101₂, followed by 6, 7 and 9 (sequence A052294 in OEIS).

Properties

Number (magazine)

Number is the leading Japanese sports magazine published on every Thursday by Bungeishunju. The official name is Sports Graphic Number. Though the circulation once hit 47 million, it is now around 10 million.

The first issue, released in April 1980, drew attention by the piece Enatsu's 21 balls (江夏の21球, Enatsu no 21 kyu). Yet the magazine failed to return a profit for the next 10 years. Today however, the magazine is one of the most profitable publications of Bungeishunju. The success of the magazine also led other rival publishers to launch sports magazines, though they tend to be less successful.

References

Grammatical number

In linguistics, grammatical number is a grammatical category of nouns, pronouns, and adjective and verb agreement that expresses count distinctions (such as "one", "two", or "three or more"). In many languages, including English, the number categories are singular and plural. Some languages also have a dual number or other arrangements.

The count distinctions typically, but not always, correspond to the actual count of the referents of the marked noun or pronoun.

The word "number" is also used in linguistics to describe the distinction between certain grammatical aspects that indicate the number of times an event occurs, such as the semelfactive aspect, the iterative aspect, etc. For that use of the term, see "Grammatical aspect".

Overview

Most languages of the world have formal means to express differences of number. One widespread distinction, found in English and many other languages, involves a simple two-way number contrast between singular and plural (car/cars, child/children, etc.). Discussion of other more elaborate systems of number appears below.

Personal Communications Services area codes

Area codes 500, 533, 544, 566 and 577 are non-geographic area codes reserved for personal communications services. The 500 code was authorized by the United States Federal Communications Commission, and introduced into the North American Numbering Plan in 1995.

In 1995 AT&T introduced a "follow-me" service under the brand name of AT&T True Connections using the 500 area code. It was designed to replace the AT&T EasyReach 700 service. Other local exchange carriers and interexchange carriers introduced similar competitive services.

AT&T True Connections service was not well received. Companies, hotels, and others with PBX equipment continued to block the dialing of 500 because it was a caller-paid number. Phone-sex services also began using the 500 prefix and forwarding the calls to various foreign countries.

The 500 prefix is still registered to a variety of phone companies, and is being used for non-geographic services including dial-up modem access.