A211203 Prime numbers p such that p-1 divides (2^(p-1)+1)*(2^p-2).

2, 3, 7, 11, 19, 31, 43, 79, 127, 151, 163, 211, 251, 271, 311, 331, 379, 487, 547, 631, 751, 811, 883, 991, 1051, 1171, 1231, 1459, 1471, 1831, 1951, 1999, 2251, 2311, 2531, 2647, 2731, 2791, 2971, 3079, 3331, 3511, 3631, 3691, 3823, 3943, 4051, 4447, 4651

Offset: 1

Author

Philip A. Hoskins, Feb 06 2013

Keywords

• nonn

Comments

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

Prime p>2 is in this sequence iff (p-1)/2 belongs to A014957. - Max Alekseyev, Dec 26 2017

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..204 from Philip A. Hoskins)

Crossrefs

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

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

Programs

Maple

A211203:=proc(q)
local n;
for n from 1 to q do
  if type((2^(2*ithprime(n)-1)-2)/(ithprime(n)-1),integer) then print(ithprime(n));
fi; od; end:
A211203(10000000); # Paolo P. Lava, Feb 18 2013

Mathematica

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

PARI

is(p) = lift((Mod(2,p-1)^(p-1)+1)*(Mod(2,p-1)^p-2))==0 \\ David A. Corneth, Mar 25 2021

Python

from sympy import primerange
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