A200510 Least m>0 such that n = 10^x-y^2 (mod m) has no solution, or 0 if no such m exists.

0, 0, 3, 5, 9, 3, 0, 9, 3, 0, 0, 3, 35, 5, 3, 11, 9, 3, 5, 0, 3, 16, 9, 3, 11, 9, 3, 20, 5, 3, 16, 9, 3, 5, 9, 3, 0, 11, 3, 0, 9, 3, 20, 5, 3, 32, 11, 3, 5, 9, 3, 0, 9, 3, 28, 37, 3, 11, 5, 3, 200, 9, 3, 5, 0, 3, 16, 9, 3, 16, 9, 3, 35, 5, 3, 0, 9, 3, 5, 9

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 A051221, i.e., not of the form 10^x-y^2. On the other hand, if n is in A051221, i.e., there are integers x, y such that n=10^x-y^2, then we know that a(n)=0.

Similar to the comment in A200522, it is likely (but still unproven) that a(n) = 0 if and only if n is in A051221. The extension by Azuma confirms that this holds for n = 0..2000. - Seiichi Azuma, Apr 04 2025

Examples

			See A200507.
		

Links

• Seiichi Azuma, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A051204-A051221, A200505-A200524.

Programs

PARI

A200510(n,b=10,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))}

Formula

a(111)=11111.