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A243885 Smallest prime p_n which generates n primes of the form (p_n^i - 4) when i runs through the first n odd numbers. 0
7, 11, 11, 971, 71394923, 959316767, 13342820302307 (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:

A046132 : Larger member p+4 of cousin primes (p, p+4).

A243817 : Primes p for which p - 4 and p^3 - 4 are primes.

A243818 : Primes p for which p^i - 4 is prime for i = 1, 3 and 5.

A243861 : Primes p for which p^i - 4 is prime for i = 1, 3, 5 and 7.

LINKS

Table of n, a(n) for n=1..7.

EXAMPLE

a(1) = 7 because 7-4 = 3 (prime),

a(2) = 11 because 11-4 = 7 (prime) and  11^3 - 4 = 1327 (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 > 0:

....al=0

....n=2

....while al!=co:

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

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

............d.append(int(n**((2*i)+1))-4)

........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. A046132, A243817, A243818 and A243861.

Sequence in context: A205679 A166980 A184071 * A171017 A195608 A228523

Adjacent sequences:  A243882 A243883 A243884 * A243886 A243887 A243888

KEYWORD

nonn,hard,more

AUTHOR

Abhiram R Devesh, Jun 13 2014

EXTENSIONS

a(6) from Bert Dobbelaere, Jul 16 2019

a(7) from Giovanni Resta, Jul 18 2019

STATUS

approved

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Last modified January 26 06:32 EST 2021. Contains 340434 sequences. (Running on oeis4.)