A271267 Even numbers k such that k + 2 divides k^k + 2.

4, 16, 196, 2836, 5956, 25936, 65536, 540736, 598816, 797476, 1151536, 3704416, 8095984, 11272276, 13362420, 21235696, 29640832, 31084096, 42913396, 49960912, 55137316, 70254724, 70836676, 81158416, 94618996, 111849956, 129275056, 150026176, 168267856, 169242676, 189796420, 192226516, 198464176, 208232116, 244553296, 246605776, 300018016, 318143296

Offset: 1

Author

Altug Alkan, Apr 03 2016

Keywords

• nonn

Comments

In other words, even numbers k such that k + 2 divides A014566(k) + 1.

Even terms of A213382.

4, 16, 65536 are the numbers of the form 2^(2^(2^k)), for k >= 0. Are there other members of this sequence with the form of 2^(2^(2^k))?

2^(2^(2^3)) and 2^(2^(2^4)) are terms. - Michael S. Branicky, Apr 16 2021

Examples

			4 is a term because 4 + 2 = 6 divides 4^4 + 2 = 258.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..150

Crossrefs

Cf. A014566, A081765, A213382.

Programs

Mathematica

Select[Range[2, 10^4, 2], Divisible[#^# + 2, # + 2] &] (* Michael De Vlieger, Apr 03 2016 *)

PARI

lista(nn) = forstep(n=2, nn, 2, if( Mod(n, n+2)^n == -2 , print1(n, ", "))); \\ Joerg Arndt, Apr 03 2016

Python

def afind(limit):
  k = 2
  while k < limit:
    if (pow(k, k, k+2) + 2)%(k+2) == 0: print(k, end=", ")
    k += 2
afind(10**7) # Michael S. Branicky, Apr 16 2021