A200506 Least m>0 such that n = 6^x-y^2 (mod m) has no solution, or 0 if no such m exists.

0, 0, 0, 5, 5, 0, 0, 9, 5, 5, 7, 0, 63, 5, 5, 36, 9, 7, 5, 5, 0, 44, 9, 5, 5, 9, 16, 0, 5, 5, 16, 7, 0, 5, 5, 0, 0, 21, 5, 5, 9, 16, 16, 5, 5, 7, 12, 0, 5, 5, 28, 36, 7, 5, 5, 12, 192, 16, 5, 5, 37, 9, 16, 5, 5, 24, 7, 9, 5, 5, 9, 0, 0, 5, 5, 36, 9, 52, 5, 5

Offset

0,4

Comments

If such an m>0 exists, this proves that n is not in A051217, i.e., not of the form 6^x-y^2. On the other hand, if there are integers x, y such that n=6^x-y^2, then we know that a(n)=0.

Links

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

Formula

a(3+5k)=a(4+5k)=5, a(10+35k)=a(17+35k)=a(31+35k)=7 for all k>=0.

a(n)=9 for n=7, 16, 22, 70, 76 and 85 (mod 90).

Example

See A200507.

Prog

(PARI) A200506(n, b=6, p=3)={ my( x=0, qr, bx, seen ); for( m=2, 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, A200522, A200523, A200524, A200505-A200520.

Sequence in context: A189232 A247667 A115144 * A285070 A285288 A356116

Adjacent sequences: A200503 A200504 A200505 * A200507 A200508 A200509

Keyword

nonn

Author

M. F. Hasler, Nov 18 2011

Status

approved