Search: id:A058429
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%I A058429
%S A058429 2,548,585688,58591812,200824138,5773251280200207952,
%T A058429 20832739723817975138362
%N A058429 Numbers n such that n^2 contains only digits {0,3,4}, not ending with 
               zero.
%H A058429 P. De Geest, <a href="http://www.worldofnumbers.com/threedigits.htm">
               Index to related sequences</a>
%H A058429 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               math02/math0210.htm#034">Sporadic tridigital solutions</a>
%o A058429 (PARI) admissibleMod(LIM=10000)={ local( t=[4], tt=1 ); while( LIM > 
               tt*=10, t=concat([t,t+vector(#t,i,3)*tt,t+vector(#t,i,4)*tt])); /
               *print("t="t);*/ t=Set(t); tt=[]; for(i=1,LIM,if( setsearch(t,i^2%LIM), 
               tt=concat(tt,i))); concat(tt,LIM+tt[1])} A058429(Nmax=1e19,N=2,addMod=100000,
               debug=1)={local( a=[], Nnext, N2, numDigits, place, addNext=admissibleMod(addMod=round(addMod)), 
               d=1, add=vector(addMod,i,if(i-1>addNext[d],d++);addNext[d]-i+1), 
               nextOK=[0,2,1,0,0,5,4,3,2,1], pow10 = vector( d=#Str((Nmax=round(Nmax))^2), 
               i, 10^(i-1)) ); nextOK = vector( #nextOK, i, if( nextOK[i],nextOK[i]*pow10)); 
               N=round(N); while( Nmax >= N, numDigits = #Str(N2=N^2); if( 3 > N2 
               \ pow10[numDigits], N = sqrtint( 3*pow10[numDigits]+3 )+1); Nnext 
               = min( Nmax, sqrtint(pow10[numDigits]*10)\3*2); 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]], 
               ); 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+1 ); N = floor(Nnext*5/2); );a } - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), 
               May 14 2007
%Y A058429 Cf. A058430.
%Y A058429 Sequence in context: A101702 A119780 A120840 this_sequence A117509 A049364 
               A159529
%Y A058429 Adjacent sequences: A058426 A058427 A058428 this_sequence A058430 A058431 
               A058432
%K A058429 nonn,base,hard
%O A058429 1,1
%A A058429 Patrick De Geest (pdg(AT)worldofnumbers.com), Nov 15 2000.
%E A058429 One more term from M. F. Hasler (Maximilian.Hasler(AT)gmail.com), May 
               14 2007
%E A058429 One more term from Mishima's page. Max Alekseyev (maxale(AT)gmail.com), 
               Jul 13 2009

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