A200506 - OEIS

%I #15 Mar 31 2012 13:48:35

%S 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,

%T 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,

%U 9,16,5,5,24,7,9,5,5,9,0,0,5,5,36,9,52,5,5

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

%C 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.

%H M. F. Hasler, <a href="/A200506/b200506.txt">Table of n, a(n) for n = 0..1000</a>

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

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

%e See A200507.

%o (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))}

%Y Cf. A051204-A051221, A200522, A200523, A200524, A200505-A200520.

%K nonn

%O 0,4

%A _M. F. Hasler_, Nov 18 2011