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A200508 Least m>0 such that n = 8^x-y^2 (mod m) has no solution, or 0 if no such m exists.

%I A200508 #10 Mar 31 2012 13:48:35
%S A200508 0,0,4,7,0,7,4,0,0,7,4,8,7,20,4,0,7,7,4,7,9,16,4,7,7,16,4,8,0,9,4,7,9,
%T A200508 7,4,8,48,7,4,0,7,9,4,8,7,7,4,7,0,20,4,7,7,12,4,0,9,16,4,7,0,7,4,0,0,
%U A200508 7,4,8,7,16,4,0,7,7,4,7,32,9,4,7,7,44,4
%N A200508 Least m>0 such that n = 8^x-y^2 (mod m) has no solution, or 0 if no such m exists.
%C A200508 If such an m>0 exists, this proves that n is not in A051219, i.e., not of the form 8^x-y^2. On the other hand, if n is in A051219, i.e., there are integers x, y such that n=8^x-y^2, then we know that a(n)=0.
%H A200508 M. F. Hasler, <a href="/A200508/b200508.txt">Table of n, a(n) for n = 0..1000</a>
%e A200508 See A200507.
%o A200508 (PARI) A200508(n,b=8,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 A200508 Cf. A051204-A051221, A200505-A200524.
%K A200508 nonn
%O A200508 0,3
%A A200508 _M. F. Hasler_, Nov 18 2011