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A242886 Smallest prime p_n which generates n primes of the form (p^i + 2) where i represents the first n odd numbers. 0
3, 3, 419, 132749, 514664471, 1164166301 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The first 4 entries of this sequence are the first entry of the following sequences:

a. A001359: Lesser of twin primes.

b. A240110: Primes p such that p + 2 and p^3 + 2 are also prime.

c. A242326: Primes p for which p + 2, p^3 + 2, and p^5 + 2 are also prime.

d. A242327: Primes p for which (p^n) + 2 is prime for n = 1, 3, 5, and 7.

LINKS

Table of n, a(n) for n=1..6.

EXAMPLE

For n = 1, p = 3 generates primes of the form p^n + 2; for i = 1,

   p + 2 = 5 (prime).

For n = 2, p = 3 generates primes of the form p^n + 2; for i = 1 and 3,

   p + 2 = 5 (prime) and p^3 + 2 = 29 (prime).

For n = 3, p = 419 generates primes of the form p^n + 2; for i = 1, 3, and  5, p + 2 = 421 (prime), p^3 + 2 = 73560061 (prime), and p^5 + 2 = 12914277518101 (prime).

PROG

(Python)

import sympy

## isp_list returns an array of true/false for prime number test for a

## list of numbers

def isp_list(ls):

....pt=[]

....for a in ls:

........if sympy.ntheory.isprime(a)==True:

............pt.append(True)

....return(pt)

co=1

while co < 7:

....al=0

....n=2

....while al!=co:

........d=[]

........for i in range(0, co):

............d.append(int(n**((2*i)+1))+2)

........al=isp_list(d).count(True)

........if al==co:

............## Prints prime number and its corresponding sequence d

............print(n, d)

........n=sympy.ntheory.nextprime(n)

....co=co+1

CROSSREFS

Cf. A001359, A240110, A242326, A242327.

Sequence in context: A009715 A335258 A292163 * A221947 A138662 A009011

Adjacent sequences:  A242883 A242884 A242885 * A242887 A242888 A242889

KEYWORD

nonn,hard,more

AUTHOR

Abhiram R Devesh, May 25 2014

STATUS

approved

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Last modified August 4 06:58 EDT 2020. Contains 336201 sequences. (Running on oeis4.)