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 A057129 #13 Apr 19 2025 18:03:35
%S A057129 1,2,4,5,8,10,13,17,20,25,26,29,34,37,40,41,50,52,53,58,61,65,68,73,
%T A057129 74,82,85,89,97,100,101,104,106,109,113,116,122,125,130,136,137,145,
%U A057129 146,148,149,157,164,169,170,173,178,181,185,193,194,197,200,202,205,212
%N A057129 -4 is a square mod n.
%C A057129 Numbers that are not multiples of 16 and for which all odd prime factors are congruent to 1 mod 4. - _Eric M. Schmidt_, Apr 21 2013
%H A057129 Eric M. Schmidt, <a href="/A057129/b057129.txt">Table of n, a(n) for n = 1..1000</a>
%t A057129 Select[Range[100], IntegerQ[PowerMod[-4, 1/2, #]] &] // Quiet (* After Jean-François Alcover *) (* _Robert Price_, Apr 19 2025 *)
%o A057129 (Sage)
%o A057129 def A057129(n) :
%o A057129 if n%16==0: return False
%o A057129 for (p, m) in factor(n) :
%o A057129 if p % 4 not in [1, 2] : return False
%o A057129 return True
%o A057129 # _Eric M. Schmidt_, Apr 21 2013
%Y A057129 Includes the primes in A002313 and these (primes congruent to {1, 2} mod 4) are the prime factors of the terms in this sequence. Cf. A008784, A057125, A057126, A057127, A057128.
%K A057129 nonn
%O A057129 1,2
%A A057129 _Henry Bottomley_, Aug 10 2000