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.

7, 11, 11, 971, 71394923, 959316767, 13342820302307

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