A247220 Numbers k such that k^2 + 1 divides 2^k + 1.

0, 2, 4, 386, 20136, 59140, 373164544

Offset: 1

Author

Juri-Stepan Gerasimov, Nov 26 2014

Keywords

• nonn
• more

Comments

a(8) > 10^12. - Giovanni Resta, May 05 2020

All terms of the sequence are even. a(5), a(6) and a(7) are of the form 2*p + 2 where p is a prime and p mod 14 = 1. - Farideh Firoozbakht, Dec 07 2014

From Jianing Song, Jan 13 2019: (Start)

Among the known terms only a(3) and a(4) are of the form 2*p where p is a prime.

a(n)^2 + 1 is prime for 2 <= n <= 7. Among these primes, the multiplicative order of 2 modulo a(n)^2 + 1 is 2*a(n) except for n = 5, in which case it is 2*a(n)/3. (End)

If a(n)^2 + 1 is composite, then a(n) is also a term of A135590. - Max Alekseyev, Apr 25 2024

Examples

			0 is in this sequence because 0^2 + 1 = 1 divides 2^0 + 1 = 2.
		

Crossrefs

Cf. A135590, A247165.

Programs

PARI

for(n=0,10^5,if(Mod(2,n^2+1)^n==-1,print1(n,", "))); \\ Joerg Arndt, Nov 30 2014

Python

from gmpy2 import powmod
A247220_list = [i for i in range(10**7) if powmod(2,i,i*i+1) == i*i]
# Chai Wah Wu, Dec 03 2014

Extensions

a(7) from Hiroaki Yamanouchi, Nov 29 2014