A243885 - OEIS

%I #16 Jul 18 2019 02:53:39

%S 7,11,11,971,71394923,959316767,13342820302307

%N Smallest prime p_n which generates n primes of the form (p_n^i - 4) when i runs through the first n odd numbers.

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

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

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

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

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

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

%e a(2) = 11 because 11-4 = 7 (prime) and  11^3 - 4 = 1327 (prime).

%o (Python)

%o import sympy

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

%o ## list of numbers

%o def isp_list(ls):

%o ....pt=[]

%o ....for a in ls:

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

%o ............pt.append(True)

%o ....return(pt)

%o co=1

%o while co > 0:

%o ....al=0

%o ....n=2

%o ....while al!=co:

%o ........d=[]

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

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

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

%o ........if al==co:

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

%o ............print(n, d)

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

%o ....co=co+1

%Y Cf. A046132, A243817, A243818 and A243861.

%K nonn,hard,more

%O 1,1

%A _Abhiram R Devesh_, Jun 13 2014

%E a(6) from _Bert Dobbelaere_, Jul 16 2019

%E a(7) from _Giovanni Resta_, Jul 18 2019