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A243818
Primes p for which p^i - 4 is prime for i = 1, 3 and 5.
3
11, 971, 1877, 2861, 8741, 12641, 13163, 16763, 28283, 29021, 30707, 36713, 41957, 42227, 58967, 98717, 105971, 115127, 128663, 138641, 160817, 164093, 167441, 190763, 205607, 210173, 211067, 228341, 234197, 237977, 246473, 249107, 276557, 295433, 312233
OFFSET
1,1
COMMENTS
This is a subsequence of the following:
A046132: Larger member p+4 of cousin primes (p, p+4).
A243817: Primes p for which p - 4 and p^3 - 4 are primes.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..250 from Abhiram R Devesh)
EXAMPLE
p = 11 is in this sequence because p - 4 = 7 (prime), p^3 - 4 = 1327 (prime) and p^5 - 4 = 161047 (prime).
p = 971 is in this sequence because p - 4 = 967 (prime), p^3 - 4 = 915498607 (prime) and p^5 - 4 = 863169625893847 (prime).
MATHEMATICA
Select[Range[300000], PrimeQ[#] && AllTrue[#^{1, 3, 5} - 4, PrimeQ] &] (* Amiram Eldar, Apr 04 2020 *)
Select[Prime[Range[27000]], AllTrue[#^{1, 3, 5}-4, PrimeQ]&] (* Harvey P. Dale, Jan 04 2021 *)
PROG
(Python)
import sympy.ntheory as snt
n=5
while n>1:
....n1=n-4
....n2=((n**3)-4)
....n3=((n**5)-4)
....##Check if n1 , n2 and n3 are also primes.
....if snt.isprime(n1)== True and snt.isprime(n2)== True and snt.isprime(n3)== True:
........print(n, n1, n2, n3)
....n=snt.nextprime(n)
CROSSREFS
Sequence in context: A083816 A233092 A302374 * A278864 A281285 A278719
KEYWORD
nonn,easy
AUTHOR
Abhiram R Devesh, Jun 11 2014
STATUS
approved