A051221 Numbers of the form 10^x-y^2 >= 0.

0, 1, 6, 9, 10, 19, 36, 39, 51, 64, 75, 84, 91, 96, 99, 100, 144, 159, 199, 216, 271, 324, 375, 396, 424, 471, 516, 559, 591, 600, 639, 676, 711, 744, 775, 784, 804, 831, 856, 879, 900, 919, 936, 951, 964, 975, 984, 991, 996, 999, 1000, 1164, 1351, 1404, 1536, 1719, 1756, 1900, 1999

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

The values <= 2000 listed in this sequence are obtained from x <= 7. Seiichi Azuma proved that the list is complete up to 2000. - Seiichi Azuma, Apr 02 2025

Links

• Seiichi Azuma, Elementary Proof of the Completeness of OEIS A051221 Below 2000, arXiv:2504.00116 [math.NT], 2025. See pp. 1, 4.

Crossrefs

Cf. A128826.

Programs

Mathematica

(* This program is unsafe and should not be used to extend the sequence. *)
max = 2000; Clear[f]; f[m_] := f[m] = Select[Table[10^x - y^2, {x, 0, m}, {y, 0, Ceiling[10^(x/2)]}] // Flatten // Union, 0 <= # <= max &]; f[1]; f[m = 2]; While[f[m] != f[m - 1], m++]; Print["m = ", m]; A051221 = f[m] (* Jean-François Alcover, May 13 2017 *)