A058429 Numbers k such that k^2 contains only digits {0,3,4}, not ending with zero.

2, 548, 585688, 58591812, 200824138, 5773251280200207952, 20832739723817975138362

Offset

1,1

Links

Table of n, a(n) for n=1..7.

Patrick De Geest, Index to related sequences

Hisanori Mishima, Sporadic tridigital solutions

Prog

(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, setsearch(t, i^2%LIM) && tt=concat(tt, i)); concat(tt, LIM+tt[1])}
A058429(Nmax=1e19, N=2, addMod=100000, debug=1)={my( 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); 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]], ); place || break; N = sqrtint( N2 - dr[2] + d[ place ])+1; N+=add[1+N%addMod]); if( !place, debug && print( N, "^2 = ", N^2); a=concat(a, N); N=Nnext+1 ); N=Nnext*5\2); a } \\ M. F. Hasler, May 14 2007, edited Nov 14 2017

Crossrefs

Cf. A058430.

Sequence in context: A120840 A348174 A348003 * A336784 A201247 A265633

Adjacent sequences: A058426 A058427 A058428 * A058430 A058431 A058432

Keyword

nonn,base,hard

Author

Patrick De Geest, Nov 15 2000

Extensions

a(6) from M. F. Hasler, May 14 2007

a(7) from Mishima's page added by Max Alekseyev, Jul 13 2009

Status

approved