cp's OEIS Frontend

A200524 Least m>0 such that n = 4^x-y^2 (mod m) has no solution, or 0 if no such m exists.

%I A200524 #10 Mar 31 2012 13:48:35
%S A200524 0,0,3,0,0,3,4,0,3,16,4,3,0,20,3,0,0,3,4,56,3,16,4,3,80,16,3,40,0,3,4,
%T A200524 0,3,20,4,3,64,16,3,0,63,3,4,56,3,28,4,3,0,20,3,40,63,3,4,0,3,16,4,3,
%U A200524 0,28,3,0,0,3,4,40,3,16,4,3,85,16,3,56,63,3
%N A200524 Least m>0 such that n = 4^x-y^2 (mod m) has no solution, or 0 if no such m exists.
%C A200524   If such an m>0 exists, this proves that n is not in A051215, i.e., not of the form 4^x-y^2. On the other hand, if there are integers x, y such that n=4^x-y^2, then we know that a(n)=0.
%C A200524 Some of the larger values include a(303)= 1387, a(423)=1687, a(447)=2047, a(519)>30000.
%H A200524 M. F. Hasler, <a href="/A200524/b200524.txt">Table of n, a(n) for n = 0..518</a>
%e A200524 See A200507 for motivation and examples.
%o A200524 (PARI) A200524(n,b=4,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 A200524 Cf. A051204-A051221, A200522, A200523, A200505-A200520.
%K A200524 nonn
%O A200524 0,3
%A A200524 _M. F. Hasler_, Nov 18 2011