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

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, 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, 15, 0, 4, 4, 8, 45, 4, 4, 0, 15, 4, 4, 8, 0, 4, 4, 0, 0, 4

Offset: 0

Author

M. F. Hasler, Nov 18 2011

Keywords

• nonn

Comments

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.

Examples

			See A200507.
		

Links

• M. F. Hasler, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A051204-A051221, A200505-A200524.

Programs

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 & break; next(3))); return(m))}