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 A227784 #6 Aug 01 2013 11:20:45 %S A227784 0,1,2,3,4,2,2,7,2,4,2,3,2,2,4,15,1,2,2,4,2,2,2,7,4,2,2,3,3,4,2,15,2, %T A227784 1,4,3,2,2,2,7,1,2,2,3,4,2,2,15,2,4,2,3,2,2,4,7,2,3,2,4,2,2,2,15,4,2, %U A227784 2,3,2,4,2,7,1,2,4,3,2,2,2,15,2,1,2,3,4,2,3,7,1,4,2 %N A227784 Least number of fourth powers which add to -1 mod n. %C A227784 Parnami, Agrawal, & Rajwade proved (1981, Theorem 1) that, for a prime p > 29, a(p) = 1 if p = 1 mod 8 and otherwise a(p) = 2. %C A227784 Conjecture: a(n) = 15 if n = 9 mod 16 and a(n) = 7 if n = 8 mod 16, otherwise a(n) <= 4. (The associated lower bounds are obvious.) %D A227784 J. C. Parnami, M. K. Agrawal, and A. R. Rajwade, On the 4-power Stufe of a field, Rendiconti del Circolo Matematico di Palermo (2) 30:2 (1981), pp. 245-254. %H A227784 Charles R Greathouse IV, <a href="/A227784/b227784.txt">Table of n, a(n) for n = 1..10000</a> %H A227784 J. C. Parnami, M. K. Agrawal, and A. R. Rajwade, <a href="http://seminariomatematico.dm.unito.it/rendiconti/cartaceo/44-1/141.pdf">On the 4-power Stufe of p-adic completions of algebraic number fields</a>, Rendiconti del Seminario Matematico Università e Politecnico di Torino 44:1 (1986), pp. 141-153. %F A227784 a(n) <= A002377(n-1) <= 19. %F A227784 a(n) = 1 if and only if n > 1 is in A192453. %o A227784 (PARI) a(n)=if(n==1,return(0)); if(n>29 && isprime(n), return(if(n%8>1, 2, 1))); my(N,cur,new,k=1);for(i=1,n\2,cur=N=bitor(1<<(i^4%n),N));while(!bittest(cur,n-1),new=0;for(i=1,n\2,t=cur<<(i^4%n);t=bitor(bitand(t,(1<<n)-1),t>>n);new=bitor(new,t));k++;cur=new);k %Y A227784 Cf. A192453, A227781. %K A227784 nonn %O A227784 1,3 %A A227784 _Charles R Greathouse IV_, Aug 01 2013