A200522 - OEIS

%I #13 Oct 23 2014 10:30:18

%S 0,0,0,0,0,15,12,0,0,20,16,24,0,32,20,0,0,28,12,56,15,16,16,0,112,68,

%T 16,40,0,20,12,0,0,52,20,15,80,16,16,0,112,36,12,56,33,28,28,0,0,20,

%U 15,40,128,16,12,0,117,48,16,24,0,44,28,0,0,15,12,40,63

%N Least m>0 such that n = 2^x-y^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 A051213, i.e., not of the form 2^x-y^2. On the other hand, if there are integers x, y such that n=2^x-y^2, then we know that a(n)=0.

%C a(519) > 20000 if it is nonzero.

%C It remains to show whether "a(n)=0" is equivalent to "n is in A051213". For example, one can show that 519 is not in A051213, but we don't know a(519) yet. - _M. F. Hasler_, Oct 23 2014

%H M. F. Hasler, <a href="/A200522/b200522.txt">Table of n, a(n) for n = 0..518</a>

%e See A200507 for motivation and examples.

%o (PARI) A200522(n,b=2,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, A200523, A200524, A200505-A200520.

%K nonn

%O 0,6

%A _M. F. Hasler_, Nov 18 2011