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A243269
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Smallest prime p such that p^k - 2 is prime for all odd exponents k from 1 up to 2*n-1 (inclusive).
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0
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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