%I A058433
%S A058433 3,969071253
%N A058433 Numbers n such that n^2 contains only digits {0,3,9}, not ending with 
               zero.
%C A058433 No more terms up to 10^23. - Charles R Greathouse IV, Jul 27 2009
%H A058433 P. De Geest, <a href="http://www.worldofnumbers.com/threedigits.htm">
               Index to related sequences</a>
%H A058433 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               math02/math0210.htm#039">Sporadic tridigital solutions</a>
%o A058433 (PARI) admissibleMod(M=1000,t=[3,9],debug=0)={ local( tt=1 ); while( 
               M > tt*=10, t=concat([t,t+vector(#t,i,t[1])*tt,t+vector(#t,i,t[2])*tt])); 
               if( debug, print("t="t)); t=Set(t); tt=[];
%o A058433 for(i=1,M,if( setsearch(t,i^2%M), tt=concat(tt,i))); concat(tt,M+tt[1])} 
               A058433(Nmax=1e10,N=1,addMod=100000, debug=1)={ local( a=[], addNext=admissibleMod(addMod=10^round(log(ad\
               dMod)/log(10)),[3,9]), d=1, add=vector(addMod,i,if(i-1>addNext[d],
               d++);addNext[d]-i+1), pow10 = vector( d=#Str((Nmax=round(Nmax))^2), 
               i, 10^(i-1)), nextOK=[0,2,1,0,5,4,3,2,1,0], Nnext, N2, numDigits, 
               place );
%o A058433 nextOK = vector( #nextOK, i, if( nextOK[i],nextOK[i]*pow10)); N=round(N); 
               while( Nmax >= N, numDigits = #Str(N2=N^2); if( place = nextOK[1+ 
               d=N2 \ pow10[numDigits] ], N = max(sqrtint( place[numDigits]+d*pow10[numDigits] 
               ),N+1); next); Nnext = min( Nmax, sqrtint( round((d+1)*pow10[numDigits]) 
               ));
%o A058433 if( debug, print( "checking from "N" to "Nnext": <= ",1+max(0,Nnext-N)*(#addNext-1)\ 
               addMod," candidates.")); N += add[1+ N%addMod]; place=1; while( Nnext 
               >= N, dr = divrem( N2=N^2, pow10[ place=numDigits ] ); while( place-- 
               & !d=nextOK[1+ (dr = divrem( dr[2], pow10[ place ] ))[1]], );
%o A058433 if( !place, break); N = sqrtint( N2 - dr[2] + d[ place ])+1; N+=add[1+N%addMod]; 
               ); if( !place, if( debug, print( N, "^2 = ", N^2 )); a=concat(a,N)); 
               N = Nnext*3\2+1 );a} - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), 
               May 14 2007
%Y A058433 Cf. A058434.
%Y A058433 Sequence in context: A058469 A081508 A067481 this_sequence A154998 A036236 
               A058447
%Y A058433 Adjacent sequences: A058430 A058431 A058432 this_sequence A058434 A058435 
               A058436
%K A058433 nonn,base,hard,more,bref
%O A058433 1,1
%A A058433 Patrick De Geest (pdg(AT)worldofnumbers.com), Nov 15 2000.