A197722 Smallest number k such that k^2 begins with n^3.

1, 9, 52, 8, 112, 147, 586, 716, 27, 100, 1154, 4157, 4688, 5239, 581, 64, 22166, 2415, 2619, 28285, 30432, 10319, 34882, 37181, 125, 41924, 44366, 46853, 15617, 51962, 54582, 18102, 59948, 62693, 207063, 216, 71171, 74076, 77019, 800, 83019, 272192, 28197

Offset: 1

Author

Michel Lagneau, Oct 17 2011

Keywords

• nonn
• base

Examples

			a(6) = 147 because 147^2 = 21609 starts with 216 = 6^3.
		

Crossrefs

See A138173 (smallest m such that m^3 begins with n^2).

Programs

Mathematica

f[n_]:=Block[{k = 0, m}, While[m = Max[0, Floor@Log[10, k^2]-Floor@Log[10, n^3]]; (k^2-Mod[k^2, 10^m])/10^m != n^3, k++]; k]; Array[f, 43]