A237642 - OEIS

%I #11 Feb 27 2023 14:47:13

%S 5,11,29,71,131,181,379,419,599,1979,2069,3191,4159,13339,14519,17291,

%T 19739,20879,21169,26731,30449,31151,39799,48619,69959,70489,112559,

%U 122849,132859,139501,149381,183611,186191,198469,212981,222311,236681

%N Primes of the form n^2-n-1 (for some n) such that p^2-p-1 is also prime.

%C Except a(1), all numbers are congruent to 1 mod 10 or 9 mod 10.

%H Harvey P. Dale, <a href="/A237642/b237642.txt">Table of n, a(n) for n = 1..1000</a>

%e 11 is prime and equals 4^2-4-1, and 11^2-11-1 = 109 is prime. So, 11 is a member of this sequence.

%t Select[Table[n^2-n-1,{n,500}],AllTrue[{#,#^2-#-1},PrimeQ]&] (* _Harvey P. Dale_, Feb 27 2023 *)

%o (Python)

%o import sympy

%o from sympy import isprime

%o {print(n**2-n-1) for n in range(10**3) if isprime(n**2-n-1) and isprime((n**2-n-1)**2-(n**2-n-1)-1)}

%o (PARI)

%o s=[]; for(n=1, 1000, p=n^2-n-1; if(isprime(p) && isprime(p^2-p-1), s=concat(s, p))); s \\ _Colin Barker_, Feb 11 2014

%Y Cf. A002327, A091568.

%K nonn

%O 1,1

%A _Derek Orr_, Feb 10 2014