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Integer sequence prime : ウィキペディア英語版
Integer sequence prime
In mathematics, an integer sequence prime is a prime number found as a member of an integer sequence. For example, the 8th Delannoy number, 265729, is prime. A challenge in empirical mathematics is to identify large prime values in rapidly growing sequences.
A common subclass of integer sequence primes are constant primes, formed by taking a constant real number and considering prefixes of its decimal representation, omitting the decimal point. For example, the first 6 decimal digits of the constant ''π'', approximately 3.14159265, form the prime number 314159, which is therefore known as a pi-prime. Similarly, a constant prime based on ''e'' is called an e-prime.
Other examples of integer sequence primes include:
* Cullen prime – a prime that appears in the sequence of Cullen numbers a_n=n2^n+1\, .
* Factorial prime – a prime that appears in either of the sequences a_n=n!-1 or b_n=n!+1\, .
* Fermat prime – a prime that appears in the sequence of Fermat numbers a_n=2^+1\, .
* Fibonacci prime – a prime that appears in the sequence of Fibonacci numbers.
* Lucas prime – a prime that appears in the Lucas numbers.
* Mersenne prime – a prime that appears in the sequence of Mersenne numbers a_n=2^n-1\, .
* Primorial prime – a prime that appears in either of the sequences a_n=n\#-1 or b_n=n\#+1\, .
* Pythagorean prime – a prime that appears in the sequence a_n=4n+1\, .
* Woodall prime – a prime that appears in the sequence of Woodall numbers a_n=n2^n-1\, .
The On-Line Encyclopedia of Integer Sequences includes many sequences corresponding to the prime subsequences of well-known sequences, for example A001605 for Fibonacci numbers that are prime.
== References ==

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抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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