A242518 Primes p for which p^n - 2 is prime for n = 1, 3, 5 and 7.

201829, 2739721, 6108679, 7883329, 9260131, 9309721, 9917389, 14488249, 15386491, 15876481, 16685299, 16967191, 18145279, 20566969, 20869129, 21150991, 23194909, 25510189, 28406929, 34669909, 35039311, 36795169, 37912141, 39083521, 39805639

Offset

1,1

Comments

This is a subsequence of A242517.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..150 (first 100 terms from Abhiram R Davesh)

Example

p = 201829  (prime)
p - 2 = 201827 (prime)
p^3 - 2 = 8221493263045787 (prime)
p^5 - 2 = 334902077869420623790640147 (prime)
p^7 - 2 = 13642217803107967058507788317851080907 (prime)

Mathematica

Select[Prime[Range[25*10^5]], AllTrue[#^{1, 3, 5, 7}-2, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 26 2015 *)

Prog

(Python)
import sympy
n=2
while n>1:
....n1=n-2
....n2=((n**3)-2)
....n3=((n**5)-2)
....n4=((n**7)-2)
....##.Check if n1, n2, n3 and n4 are also primes
....if sympy.ntheory.isprime(n1)== True and sympy.ntheory.isprime(n2)== True and sympy.ntheory.isprime(n3)== True and sympy.ntheory.isprime(n4)== True:
........print(n, " , " , n1, " , ", n2, " , ", n3, " , ", n4)
....n=sympy.ntheory.nextprime(n)

Crossrefs

Cf. A242517, A240126, A001359, A006512.

Sequence in context: A252498 A355332 A274815 * A235929 A172623 A172728

Adjacent sequences: A242515 A242516 A242517 * A242519 A242520 A242521

Keyword

nonn

Author

Abhiram R Devesh, May 17 2014

Status

approved