A200508 Least m>0 such that n = 8^x-y^2 (mod m) has no solution, or 0 if no such m exists.

0, 0, 4, 7, 0, 7, 4, 0, 0, 7, 4, 8, 7, 20, 4, 0, 7, 7, 4, 7, 9, 16, 4, 7, 7, 16, 4, 8, 0, 9, 4, 7, 9, 7, 4, 8, 48, 7, 4, 0, 7, 9, 4, 8, 7, 7, 4, 7, 0, 20, 4, 7, 7, 12, 4, 0, 9, 16, 4, 7, 0, 7, 4, 0, 0, 7, 4, 8, 7, 16, 4, 0, 7, 7, 4, 7, 32, 9, 4, 7, 7, 44, 4

Offset

0,3

Comments

If such an m>0 exists, this proves that n is not in A051219, i.e., not of the form 8^x-y^2. On the other hand, if n is in A051219, i.e., there are integers x, y such that n=8^x-y^2, then we know that a(n)=0.

Links

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

Example

See A200507.

Prog

(PARI) A200508(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, i, i^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))}

Crossrefs

Cf. A051204-A051221, A200505-A200524.

Sequence in context: A195791 A331790 A200388 * A020833 A197147 A153117

Adjacent sequences: A200505 A200506 A200507 * A200509 A200510 A200511

Keyword

nonn

Author

M. F. Hasler, Nov 18 2011

Status

approved