Philip A. Hoskins - cp's OEIS frontend

User: Philip A. Hoskins

Philip A. Hoskins has authored 2 sequences.

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

Philip A. Hoskins, Feb 06 2013

nonn

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

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

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

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

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

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

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

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

A211349 Primes p such that p-1 divides 2^p + 2.

Original entry on oeis.org

2, 3, 11, 251, 5051, 16811, 2025251, 8751251, 16607051, 28257611, 69005051, 78906251, 176775251, 210381251, 372175451, 550427051, 707025251, 854704451, 1866788051, 2441406251, 2605806251, 4249701251, 5469531251, 9304386251, 10315761251, 10915095251

Offset: 1

Philip A. Hoskins, Feb 06 2013

nonn

Prime p>2 is in this sequence iff (p-1)/2 is in A015950. - Max Alekseyev, Dec 26 2017

Max Alekseyev, Table of n, a(n) for n = 1..177

Cf. A069051, A211203.

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

N=10^9;
default(primelimit,N);
forprime(p=2,N, if (-2==Mod(2,p-1)^p, print1(p,", ")));
/* Joerg Arndt, Feb 06 2013 */

from sympy import primerange
A211349_list = [p for p in primerange(1,10**6) if p == 2 or pow(2,p,p-1) == p-3] # Chai Wah Wu, Mar 25 2021

a(19)-a(47) from Giovanni Resta, Feb 10 2013

a(48)-a(177) from Max Alekseyev, Jan 06 2018

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User: Philip A. Hoskins

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

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