A243818 Primes p for which p^i - 4 is prime for i = 1, 3 and 5.

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

Cf. A046132, A243817.

Sequence in context: A083816 A233092 A302374 * A278864 A281285 A278719

Adjacent sequences: A243815 A243816 A243817 * A243819 A243820 A243821

Keyword

nonn,easy

Author

Abhiram R Devesh, Jun 11 2014

Status

approved