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A243269
Smallest prime p such that p^k - 2 is prime for all odd exponents k from 1 up to 2*n-1 (inclusive).
0
5, 19, 31, 201829, 131681731, 954667531, 8998333416049
OFFSET
1,1
COMMENTS
The first 4 entries of this sequence are the first entry of the following sequences:
A006512 : Primes p such that p - 2 is also prime.
A240126 : Primes p such that p - 2 and p^3 - 2 are also prime.
A242517 : Primes p such that p - 2, p^3 - 2 and p^5 - 2 are primes.
A242518 : Primes p such that p - 2, p^3 - 2, p^5 - 2 and p^7 - 2 are primes.
EXAMPLE
For n = 1, p = 5, p - 2 = 3 is prime.
For n = 2, p = 19, p - 2 = 17 and p^3 - 2 = 6857 are primes.
For n = 3, p = 31, p - 2 = 29, p^3 - 2 = 29789, and p^5 - 2 = 28629149 are primes.
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
KEYWORD
nonn,hard,more
AUTHOR
Abhiram R Devesh, Jun 02 2014
EXTENSIONS
a(7) from Bert Dobbelaere, Aug 30 2020
STATUS
approved