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A015950 Numbers k such that k | 4^k + 1.

%I A015950 #57 Sep 08 2022 08:44:40
%S A015950 1,5,25,125,205,625,1025,2525,3125,5125,8405,12625,15625,25625,42025,
%T A015950 63125,78125,103525,128125,168305,202525,210125,255025,315625,344605,
%U A015950 390625,517625,640625,841525,875125,1012625,1050625,1275125
%N A015950 Numbers k such that k | 4^k + 1.
%C A015950 From _Robert Israel_, Sep 14 2017: (Start)
%C A015950 All terms except 1 are congruent to 5 mod 20.
%C A015950 If k is a term and prime p | k, then k*p is a term.
%C A015950 All prime factors of terms == 1 (mod 4).
%C A015950 If p is a prime == 1 (mod 4) and the order of 4 (mod p) is 2*m where m is in the sequence, then m*p is in the sequence. (End)
%H A015950 Max Alekseyev, <a href="/A015950/b015950.txt">Table of n, a(n) for n = 1..3514</a> (first 325 terms from Robert Israel)
%e A015950 4^5 + 1 = 1025 and 1025 is divisible by 5, so 5 is a term.
%p A015950 select(n -> 4 &^ n + 1 mod n = 0, [1, seq(i,i=5..10^7,20)]); # _Robert Israel_, Sep 14 2017
%t A015950 Select[Prepend[20 Range[0, 10^5] + 5, 1], Mod[4^# + 1, #] == 0 &] (* _Michael De Vlieger_, Dec 31 2018 *)
%o A015950 (PARI) is_A015950(n) = Mod(4,n)^n == -1; \\ _Michel Marcus_, Sep 15 2017
%o A015950 (Magma) [n: n in [1..10^6] | Modexp(4, n, n)+1 eq n]; // _Jinyuan Wang_, Dec 29 2018
%o A015950 (Python)
%o A015950 A015950_list = [n for n in range(1,10**6) if pow(4,n,n) == n-1] # _Chai Wah Wu_, Mar 25 2021
%Y A015950 Cf. A015945, A211349.
%Y A015950 Column k=4 of A333429.
%K A015950 nonn
%O A015950 1,2
%A A015950 _Robert G. Wilson v_