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 A073503 #18 Jul 01 2013 08:49:46 %S A073503 5,10,13,15,16,17,20,25,26,29,30,32,34,35,37,39,40,41,45,48,50,51,52, %T A073503 53,55,58,60,61,64,68,70,73,74,75,78,82,87,89,90,91,95,96,97,100,101, %U A073503 102,104,105,106,109,110,111,112,113,115,116,117,119,120,122,123,125 %N A073503 Numbers n such that the number of solutions to x^4 == 1 (mod n) is twice the number of solutions of x^2 == 1 (mod n). %C A073503 Conjectures: 2n > a(n) or 2n < a(n) for infinitely many values of n and abs(a(n)-2n) < sqrt(n) for n > 45. a(n)=2n for n = 318, 338, 350, 488, 490, 492, 494,... %C A073503 Numbers divisible by 16 which have no prime factors = 1 mod 4, together with numbers not divisible by 16 which have exactly one prime factor = 1 mod 4. This refutes the conjectures. - _Charles R Greathouse IV_, Apr 16 2012 %H A073503 Charles R Greathouse IV, <a href="/A073503/b073503.txt">Table of n, a(n) for n = 1..10000</a> %F A073503 a(n) seems to be asymptotic to 2n. %t A073503 Select[Range[3, 125], Length[Reduce[x^4 - 1 == 0, x, Modulus -> #]] == 2*Length[Reduce[x^2 - 1 == 0, x, Modulus -> #]] &] (* _Jayanta Basu_, Jul 01 2013 *) %o A073503 (PARI) is(n)=my(v=factor(n)[,1]%4, s=sum(i=1,#v,v[i]==1), e=valuation(n, 2)); s==(e<4) \\ _Charles R Greathouse IV_, Apr 16 2012 %Y A073503 Cf. A060594, A073103. %K A073503 easy,nonn %O A073503 1,1 %A A073503 _Benoit Cloitre_, Aug 19 2002