A211203 - OEIS

%I #44 Mar 26 2021 12:38:33

%S 2,3,7,11,19,31,43,79,127,151,163,211,251,271,311,331,379,487,547,631,

%T 751,811,883,991,1051,1171,1231,1459,1471,1831,1951,1999,2251,2311,

%U 2531,2647,2731,2791,2971,3079,3331,3511,3631,3691,3823,3943,4051,4447,4651

%N Prime numbers p such that p-1 divides (2^(p-1)+1)*(2^p-2).

%C This is also the set of primes such that n^(4^(p-1)) is congruent to n or -n modulo p.

%C Prime p>2 is in this sequence iff (p-1)/2 belongs to A014957. - _Max Alekseyev_, Dec 26 2017

%H Chai Wah Wu, <a href="/A211203/b211203.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..204 from Philip A. Hoskins)

%p A211203:=proc(q)

%p local n;

%p for n from 1 to q do

%p   if type((2^(2*ithprime(n)-1)-2)/(ithprime(n)-1),integer) then print(ithprime(n));

%p fi; od; end:

%p A211203(10000000); # _Paolo P. Lava_, Feb 18 2013

%t Select[Prime[Range[1000]], Mod[1/2*(2^# + 2)*(2^# - 2), # - 1] == 0 &]

%o (Python)

%o from sympy import primerange

%o A211203_list = [p for p in primerange(1,10**6) if p == 2 or p == 3 or pow(2,2*p-1,p-1) == 2] # _Chai Wah Wu_, Mar 25 2021

%o (PARI) is(p) = lift((Mod(2,p-1)^(p-1)+1)*(Mod(2,p-1)^p-2))==0 \\ _David A. Corneth_, Mar 25 2021

%Y Cf. A069051 (primes p such that p - 1 divides 2^p - 2)

%Y Cf. A211349 (primes p such that p - 1 divides 2^p + 2)

%K nonn

%O 1,1

%A _Philip A. Hoskins_, Feb 06 2013