A200524 Least m>0 such that n = 4^x-y^2 (mod m) has no solution, or 0 if no such m exists.

0, 0, 3, 0, 0, 3, 4, 0, 3, 16, 4, 3, 0, 20, 3, 0, 0, 3, 4, 56, 3, 16, 4, 3, 80, 16, 3, 40, 0, 3, 4, 0, 3, 20, 4, 3, 64, 16, 3, 0, 63, 3, 4, 56, 3, 28, 4, 3, 0, 20, 3, 40, 63, 3, 4, 0, 3, 16, 4, 3, 0, 28, 3, 0, 0, 3, 4, 40, 3, 16, 4, 3, 85, 16, 3, 56, 63, 3

Offset

0,3

Comments

If such an m>0 exists, this proves that n is not in A051215, i.e., not of the form 4^x-y^2. On the other hand, if there are integers x, y such that n=4^x-y^2, then we know that a(n)=0.

Some of the larger values include a(303)= 1387, a(423)=1687, a(447)=2047, a(519)>30000.

Links

M. F. Hasler, Table of n, a(n) for n = 0..518

Example

See A200507 for motivation and examples.

Prog

(PARI) A200524(n, b=4, 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, bx=bx*b%m), for(i=1, #qr, qr[i]<bx & next; qr[i]>bx & break; next(3))); return(m))}

Crossrefs

Cf. A051204-A051221, A200522, A200523, A200505-A200520.

Sequence in context: A365462 A279168 A111787 * A308223 A222328 A222402

Adjacent sequences: A200521 A200522 A200523 * A200525 A200526 A200527

Keyword

nonn

Author

M. F. Hasler, Nov 18 2011

Status

approved