cp's OEIS Frontend

A200510 Least m>0 such that n = 10^x-y^2 (mod m) has no solution, or 0 if no such m exists.

%I A200510 #20 Apr 11 2025 17:28:18
%S A200510 0,0,3,5,9,3,0,9,3,0,0,3,35,5,3,11,9,3,5,0,3,16,9,3,11,9,3,20,5,3,16,
%T A200510 9,3,5,9,3,0,11,3,0,9,3,20,5,3,32,11,3,5,9,3,0,9,3,28,37,3,11,5,3,200,
%U A200510 9,3,5,0,3,16,9,3,16,9,3,35,5,3,0,9,3,5,9
%N A200510 Least m>0 such that n = 10^x-y^2 (mod m) has no solution, or 0 if no such m exists.
%C A200510 If such an m>0 exists, this proves that n is not in A051221, i.e., not of the form 10^x-y^2. On the other hand, if n is in A051221, i.e., there are integers x, y such that n=10^x-y^2, then we know that a(n)=0.
%C A200510 Similar to the comment in A200522, it is likely (but still unproven) that a(n) = 0 if and only if n is in A051221. The extension by Azuma confirms that this holds for n = 0..2000. - _Seiichi Azuma_, Apr 04 2025
%H A200510 Seiichi Azuma, <a href="/A200510/b200510.txt">Table of n, a(n) for n = 0..2000</a>
%F A200510 a(111)=11111.
%e A200510 See A200507.
%o A200510 (PARI) A200510(n,b=10,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))}
%Y A200510 Cf. A051204-A051221, A200505-A200524.
%K A200510 nonn
%O A200510 0,3
%A A200510 _M. F. Hasler_, Nov 18 2011