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A200509 Least m>0 such that n = 9^x-y^2 (mod m) has no solution, or 0 if no such m exists.

%I A200509 #10 Mar 31 2012 13:48:35
%S A200509 0,0,4,4,8,0,4,4,0,0,4,4,8,9,4,4,9,0,4,4,8,80,4,4,45,9,4,4,8,80,4,4,0,
%T A200509 45,4,4,8,21,4,4,9,61,4,4,8,0,4,4,45,9,4,4,8,0,4,4,0,80,4,4,8,9,4,4,
%U A200509 15,0,4,4,8,45,4,4,0,15,4,4,8,0,4,4,0,0,4
%N A200509 Least m>0 such that n = 9^x-y^2 (mod m) has no solution, or 0 if no such m exists.
%C A200509 If such an m>0 exists, this proves that n is not in A051220, i.e., not of the form 9^x-y^2. On the other hand, if n is in A051220, i.e., there are integers x, y such that n=9^x-y^2, then we know that a(n)=0.
%H A200509 M. F. Hasler, <a href="/A200509/b200509.txt">Table of n, a(n) for n = 0..1000</a>
%e A200509 See A200507.
%o A200509 (PARI) A200509(n,b=9,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,i,i^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 A200509 Cf. A051204-A051221, A200505-A200524.
%K A200509 nonn
%O A200509 0,3
%A A200509 _M. F. Hasler_, Nov 18 2011