A058433 Numbers k such that k^2 contains only digits {0,3,9}, not ending with zero.

3, 969071253

Offset

1,1

Comments

No more terms up to 10^23. - Charles R Greathouse IV, Jul 27 2009

Links

Table of n, a(n) for n=1..2.

P. De Geest, Index to related sequences

Hisanori Mishima, Sporadic tridigital solutions

Prog

(PARI) /* helper function: */
admissibleMod(M=10^5, t=[3, 9], debug=0)={ my(p=1, v); while(M > p *= 10,
    t = concat([t, t + t[1]*v=vector(#t, i, p), t + t[2]*v]));
    debug && print("t="t); t=Set(t); v=[];
    for(k=1, M, setsearch(t, k^2 % M) && v=concat(v, k)); concat(v, M+v[1])}
/* optional arguments: Nmax = upper search limit, N = start / lower limit,
   addMod = step/chunk size, debug: 0=silent, 1=verbose */
A058433(Nmax=1e10, N=1, addMod=10^5, debug=1)={ my(a=[], d=1,
  addNext = admissibleMod(addMod=10^logint(addMod\/1, 10), [3, 9]),
  add = vector(addMod, i, i-1 > addNext[d] && d++; addNext[d]-i+1),
  pow10 = [10^k | k<-[0..logint((Nmax \/= 1)^2, 10)]],
  nextOK = [if(n, n*pow10) | n<-[0, 2, 1, 0, 5, 4, 3, 2, 1, 0]]); N \/= 1;
  while( Nmax >= N, my(N2 = N^2, numDigits = logint(N2, 10)+1,
                       place = nextOK[1 + d = N2 \ pow10[numDigits]]);
    if( place, N = max(sqrtint(place[numDigits] + d*pow10[numDigits]), N+1);
               next); place = 1;
    my(Nnext = min(sqrtint((d+1)*pow10[numDigits]), Nmax));
    debug && print("checking from "N" to "Nnext": <= ",
                   1+max(0, Nnext-N)*(#addNext-1)\ addMod, " candidates.");
    while( Nnext >= N += add[1 + N % addMod],
      my(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;
    ); if( !place, debug && print(N "^2 = ", N^2); a=concat(a, N));
    N = Nnext*3\2+1); a} \\ M. F. Hasler, May 14 2007

Crossrefs

Cf. A058434 (the squares), A058429 (similar for digits {0,3,4}).

Sequence in context: A081508 A368722 A067481 * A154998 A036236 A235357

Adjacent sequences: A058430 A058431 A058432 * A058434 A058435 A058436

Keyword

nonn,base,hard,more,bref

Author

Patrick De Geest, Nov 15 2000

Status

approved