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.
%I A192453 #26 Jun 30 2025 15:30:46
%S A192453 1,2,17,34,41,73,82,89,97,113,137,146,178,193,194,226,233,241,257,274,
%T A192453 281,289,313,337,353,386,401,409,433,449,457,466,482,514,521,562,569,
%U A192453 577,578,593,601,617,626,641,673,674,697,706,761,769,802,809,818,857
%N A192453 Numbers k such that -1 is a 4th power mod k.
%C A192453 Complement of A192452. Subsequence of A008784. A further reduction to 8th powers yields 1, 2, 17, 34, 97, 113, 193, 194, ...
%C A192453 From _Jianing Song_, Mar 31 2019: (Start)
%C A192453 k is a term if and only if k is not divisible by 4 and all odd prime factors are congruent to 1 modulo 8. If k is a term of this sequence, then so are all divisors of k.
%C A192453 Decompose the multiplicative group of integers modulo k as a product of cyclic groups C_{s_1} x C_{s_2} x ... x C_{s_m}, where s_i divides s_j for i < j, then k is a term iff s_1 is divisible by 8. For k = 1 or 2, (Z/kZ)* is the trivial group, s_1 does not exist so 1 and 2 are also terms. This is an analog of A008784 (where s_1 is divisible by 4) and A319100 (where s_1 is divisible by 6). (End)
%H A192453 Jianing Song, <a href="/A192453/b192453.txt">Table of n, a(n) for n = 1..4380</a> (all terms below 10^5)
%e A192453 1^4 == -1 (mod 1). 2^4 == -1 (mod 17). 9^4 == -1 (mod 34). 3^4 == -1 (mod 41). 10^4 == -1 (mod 73).
%p A192453 select(n -> numtheory:-factorset(n) mod 8 subset {1,2}, [seq(seq(4*i+j,j=1..3),i=0..400)]); # _Robert Israel_, May 24 2019
%t A192453 Table[If[Reduce[x^4==-1,Modulus->n]===False,Null,n],{n,2,1000}]//Union
%o A192453 (PARI) for(n=1,1e3,if(ispower(Mod(-1,n),4),print1(n", "))) \\ _Charles R Greathouse IV_, Jul 03 2011
%Y A192453 Cf. A008784, A047232, A319100.
%K A192453 nonn
%O A192453 1,2
%A A192453 _José María Grau Ribas_, Jul 01 2011