%I
%S 0,0,0,0,8,0,8,9,0,0,12,0,8,9,8,20,9,0,0,12,8,80,8,0,45,9,0,0,8,80,8,
%T 9,0,45,9,20,8,21,8,80,9,80,28,9,8,0,8,0,91,9,20,36,8,0,8,12,0,80,9,
%U 80,8,9,8,28,15,0,91,9,8,45,8,0,0,15,0,20,8,0
%N Least m>0 such that n = 3^xy^2 (mod m) has no solution, or 0 if no such m exists.
%C If such an m>0 exists, this proves that n is not in A051214, i.e., not of the form 3^xy^2. On the other hand, if there are integers x, y such that n=3^xy^2, then we know that a(n)=0.
%H M. F. Hasler, <a href="/A200523/b200523.txt">Table of n, a(n) for n = 0..457</a>
%e See A200507 for developed examples.
%e Some of the larger values include a(107)=17732, a(146)=1924, a(347)=4400, a(416)=2044, a(458)>30000.
%o (PARI) A200523(n,b=3,p=3)={ my( x=0, qr, bx, seen ); for( m=3,9e9, while( x^p < m, issquare(b^xn) & return(0); x++); qr=vecsort(vector(m,y,y^2+n)%m,,8); seen=0; bx=1; until( bittest(seen+=1<<bx, bx=bx*b%m), for(i=1,#qr, qr[i]<bx & next; qr[i]>bx & break; next(3))); return(m))}
%Y Cf. A051204A051221, A200522, A200524, A200505A200520.
%K nonn
%O 0,5
%A _M. F. Hasler_, Nov 18 2011
