cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A247220 #52 Jun 27 2024 22:21:49
%S A247220 0,2,4,386,20136,59140,373164544
%N A247220 Numbers k such that k^2 + 1 divides 2^k + 1.
%C A247220 a(8) > 10^12. - _Giovanni Resta_, May 05 2020
%C A247220 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
%C A247220 From _Jianing Song_, Jan 13 2019: (Start)
%C A247220 Among the known terms only a(3) and a(4) are of the form 2*p where p is a prime.
%C A247220 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)
%C A247220 If a(n)^2 + 1 is composite, then a(n) is also a term of A135590. - _Max Alekseyev_, Apr 25 2024
%e A247220 0 is in this sequence because 0^2 + 1 = 1 divides 2^0 + 1 = 2.
%o A247220 (PARI) for(n=0,10^5,if(Mod(2,n^2+1)^n==-1,print1(n,", "))); \\ _Joerg Arndt_, Nov 30 2014
%o A247220 (Python)
%o A247220 from gmpy2 import powmod
%o A247220 A247220_list = [i for i in range(10**7) if powmod(2,i,i*i+1) == i*i]
%o A247220 # _Chai Wah Wu_, Dec 03 2014
%Y A247220 Cf. A135590, A247165.
%K A247220 nonn,more
%O A247220 1,2
%A A247220 _Juri-Stepan Gerasimov_, Nov 26 2014
%E A247220 a(7) from _Hiroaki Yamanouchi_, Nov 29 2014