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%I #9 Jan 03 2016 04:37:30
%S 0,0,8,0,8,9,0,0,0,0,8,9,8,0,9,0,0,12,8,0,8,28,0,9,0,20,8,0,8,9,20,80,
%T 9,0,8,0,8,0,9,63,0,9,8,80,8,20,0,9,0,28,8,63,8,12,0,0,9,36,8,9,8,0,
%U 12,0,532,9,8,80,8,108,20,15,0,0,8,63,8,9,0
%N Least m>0 such that n = y^2 - 3^x (mod m) has no solution, or 0 if no such m exists.
%C To prove that an integer n is in A051205, it is sufficient to find integers x,y such that y^2 - 3^x = n. In that case, a(n)=0. To prove that n is *not* in A051205, it is sufficient to find a modulus m for which the (finite) set of all possible values of 3^x and y^2 (mod m) allows us to deduce that y^2 - 3^x can never equal n. The present sequence lists the smallest such m>0, if it exists.
%e See A200512.
%o (PARI) A200513(n,b=3,p=3)={ my( x=0, qr, bx, seen ); for( m=3,9e9, while( x^p < m, issquare(b^x+n) & 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. A051204-A051221, A200505-A200520.
%K nonn
%O 0,3
%A _M. F. Hasler_, Nov 18 2011
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