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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 (list; graph; refs; listen; history; text; internal format)
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

Abhiram R Devesh, Table of n, a(n) for n = 1..250

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).

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

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Last modified October 15 04:33 EDT 2019. Contains 328026 sequences. (Running on oeis4.)