A200505 Least m>0 such that n = 5^x-y^2 (mod m) has no solution, or 0 if no such m exists.

0, 0, 4, 4, 0, 0, 4, 4, 5, 0, 4, 4, 24, 5, 4, 4, 0, 15, 4, 4, 75, 0, 4, 4, 0, 0, 4, 4, 5, 39, 4, 4, 15, 5, 4, 4, 24, 35, 4, 4, 175, 31, 4, 4, 0, 39, 4, 4, 5, 0, 4, 4, 35, 5, 4, 4, 21, 55, 4, 4, 24, 0, 4, 4, 31, 39, 4, 4, 5, 399, 4, 4, 31, 5, 4, 4, 0, 15, 4, 4

Offset

0,3

Comments

If such an m>0 exists, this proves that n is not in A051216, i.e., not of the form 5^x-y^2. On the other hand, if there are integers x, y such that n=5^x-y^2, then we know that a(n)=0.

a(144) > 20000.

Links

M. F. Hasler, Table of n, a(n) for n = 0..143

Formula

a(2+4k)=a(3+4k)=4, a(8+20k)=a(13+20k)=5 for all k>=0.

Example

See A200507.

Prog

(PARI) A200505(n, b=5, 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: A098445 A290696 A200515 * A285242 A143266 A133845

Adjacent sequences: A200502 A200503 A200504 * A200506 A200507 A200508

Keyword

nonn

Author

M. F. Hasler, Nov 18 2011

Status

approved