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 A227781 #15 May 15 2017 11:32:34 %S A227781 0,1,2,3,1,2,2,4,2,1,2,3,1,2,2,4,1,2,2,3,2,2,2,4,1,1,2,3,1,2,2,4,2,1, %T A227781 2,3,1,2,2,4,1,2,2,3,2,2,2,4,2,1,2,3,1,2,2,4,2,1,2,3,1,2,2,4,1,2,2,3, %U A227781 2,2,2,4,1,1,2,3,2,2,2,4,2,1,2,3,1,2,2,4,1,2,2,3,2,2 %N A227781 Least number of squares which add to -1 mod n. %C A227781 Pfister proved that a(p) <= 2 for all primes p; then a(p) is called the stufe of the field Z/pZ. %C A227781 Conjecture: a(n) = 4 if and only if n is divisible by 8 and a(n) = 3 if and only if n is 4 mod 8. Together with A008784 this would completely define the sequence. %D A227781 Albert Pfister, Zur Darstellung von -1 Als Summe von Quadraten in einem Korper, J. London Math. Society, 40 (1965), pp. 159-165. %D A227781 A. R. Rajwade, Squares, Cambridge Univ. Press, 1983. %H A227781 Charles R Greathouse IV, <a href="/A227781/b227781.txt">Table of n, a(n) for n = 1..10000</a> %F A227781 a(n) <= A002828(n-1) <= 4. %F A227781 a(n) = 1 if and only if n > 1 is in A008784. a(4n) >= 3 for all n. %e A227781 a(3) = 2: 1^2 + 1^2 = -1 mod 3. %e A227781 a(15) = 2: 2^2 + 5^2 = -1 mod 15. %o A227781 (PARI) isA008784(n)=if(n%2==0, if(n%4, n/=2, return(0))); n==1||vecmax(factor(n)[, 1]%4)==1 %o A227781 a(n)=if(isA008784(n),return(n>1)); if(isprime(n), return(2)); if(n%8==0, return(4)); my(N, cur, new, k=1); for(i=1,n\2,cur=N=bitor(1<<(i^2%n),N)); while(!bittest(cur,n-1), new=0; for(i=1,n\2, t=cur<<(i^2%n); t=bitor(bitand(t,(1<<n)-1), t>>n); new=bitor(new,t)); k++; cur=new); k %Y A227781 Cf. A008784, A002828. %K A227781 nonn %O A227781 1,3 %A A227781 _Charles R Greathouse IV_, Jul 31 2013