A243269 Smallest prime p such that p^k - 2 is prime for all odd exponents k from 1 up to 2*n-1 (inclusive).

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.

Links

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

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

Cf. A006512, A240126, A242517 and A242518.

Sequence in context: A347531 A356716 A262700 * A252930 A031019 A324557

Adjacent sequences: A243266 A243267 A243268 * A243270 A243271 A243272

Keyword

nonn,hard,more

Author

Abhiram R Devesh, Jun 02 2014

Extensions

a(7) from Bert Dobbelaere, Aug 30 2020

Status

approved