A241081 Numbers that are not perfect squares but that can never be ruled out as perfect squares by any final group of digits.

41, 89, 129, 161, 164, 201, 209, 241, 249, 281, 321, 329, 356, 369, 401, 409, 449, 481, 489, 516, 521, 561, 569, 601, 609, 641, 644, 649, 656, 681, 689, 721, 761, 769, 801, 804, 809, 836, 849, 881, 889, 921, 929, 964, 969, 996, 1001, 1009, 1025, 1041

Offset

1,1

Comments

All nonsquare numbers of the form 40n+1 or 40n+9 multiplied by a power of 4 times a power of 25.

Links

Table of n, a(n) for n=1..50.

Example

41 is in the sequence because there are square numbers ending in ...00041 for any number of zeros.
49 isn't in the sequence because it is a perfect square.
50 isn't in the sequence because there are no squares ending in 50.

Prog

(PARI) al(n) = {local(r=vector(n), x41, x49, i4=1, x4, i25=1, x25);
   x41=41; x49=89; x4=4*41; x25=25*41;
   for(k=1, n, r[k]=min(min(x41, x49), min(x4, x25));
      if(r[k]==x41, while(issquare(x41+=40), 0));
      if(r[k]==x49, while(issquare(x49+=40), 0));
      if(r[k]==x4, x4=4*r[i4++]);
      if(r[k]==x25, x25=25*r[i25++]));
r} \\ Franklin T. Adams-Watters, Apr 18 2014

Crossrefs

Sequence in context: A242708 A282533 A199983 * A188173 A142411 A139924

Adjacent sequences: A241078 A241079 A241080 * A241082 A241083 A241084

Keyword

nonn,base

Author

J. Lowell, Apr 15 2014

Extensions

More terms from Franklin T. Adams-Watters, Apr 18 2014

Status

approved