A257002 Primes p such that p+2 divides p^p+2.

7, 13, 19, 31, 37, 61, 67, 109, 127, 139, 157, 181, 193, 199, 211, 307, 313, 337, 379, 397, 409, 487, 499, 541, 571, 577, 631, 691, 751, 769, 787, 811, 829, 877, 919, 937, 991, 1009, 1021, 1039, 1117, 1201, 1291, 1297, 1327, 1381, 1399, 1459, 1471, 1531, 1567

Offset: 1

Author

K. D. Bajpai, Apr 14 2015

Keywords

• nonn

Comments

All the terms in this sequence are congruent to 1 mod 3.

Primes p such that 2^p == 2 (mod p+2). Includes A091180. - Robert Israel, Apr 14 2015

Examples

			a(1) = 7 is prime; 7+2 = 9 divides 7^7 + 2 = 823545.
a(2) = 13 is prime; 13+2 = 15 divides 13^13 + 2 = 302875106592255.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..5700

Crossrefs

Cf. A000040, A091180, A213382.

Programs

Magma

[ p: p in PrimesUpTo(1600) | (p^p+2) mod (p+2) eq 0 ]; // Vincenzo Librandi, Apr 15 2015

Maple

select(t -> isprime(t) and (2 &^t - 2) mod (t+2) = 0, [seq(6*i+1,i=1..10^4)]); # Robert Israel, Apr 14 2015

Mathematica

Select[Prime[Range[3000]], Mod[#^# + 2, # + 2] == 0 &]
Select[Prime[Range[500]],PowerMod[#,#,#+2]==#&] (* Harvey P. Dale, May 19 2017 *)

PARI

forprime(p=2,1000, if(Mod(p^p+2,p+2)==0, print1(p, ", ")));

Python

from sympy import prime
A257002_list = [p for p in (prime(n) for n in range(1,10**4)) if pow(p, p, p+2) == p] # Chai Wah Wu, Apr 14 2015