A200518 Least m>0 such that n = y^2-8^x (mod m) has no solution, or 0 if no such m exists.

0, 0, 4, 0, 7, 7, 4, 9, 0, 7, 4, 7, 7, 8, 4, 0, 7, 0, 4, 7, 32, 8, 4, 7, 0, 7, 4, 16, 0, 8, 4, 9, 7, 7, 4, 0, 0, 7, 4, 7, 7, 0, 4, 9, 7, 8, 4, 7, 0, 9, 4, 7, 9, 7, 4, 12, 0, 0, 4, 16, 7, 7, 4, 0, 0, 7, 4, 7, 7, 8, 4, 16, 7, 0, 4, 7, 9, 8, 4, 7, 0, 7, 4, 32

Offset: 0

Author

M. F. Hasler, Nov 18 2011

Keywords

• nonn

Comments

If a(n)>0, this proves that n cannot be a member of A051210, i.e., cannot be written as y^2-8^x. To prove that an integer n is in A051210, it is sufficient to find integers x,y such that y^2-8^x=n. In that case, a(n)=0.

Examples

			See A200512 for motivation and detailed examples.
		

Links

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

Crossrefs

Cf. A051204-A051221, A200505-A200520.

Programs

PARI

A200518(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,y,y^2-n)%m,,8); seen=0; bx=1; until( bittest(seen+=1<bx & break; next(3))); return(m))}