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a(n) is root of smallest square starting with a string of n 'digit_6's.
2

%I #6 Oct 06 2019 18:13:10

%S 8,257,2581,2582,258198,2581988,8164966,25819889,816496581,8164965809,

%T 258198889746,2581988897471,8164965809277,25819888974716,

%U 258198889747161,816496580927726,81649658092772603,2581988897471611256,8164965809277260327

%N a(n) is root of smallest square starting with a string of n 'digit_6's.

%e a(5) = 258198^2 = {66666}207204.

%t For[ i = 1, i < 20, i++, zeros = 0; isFound = False; While[ !isFound, low = Ceiling[ Sqrt[ 2/3*(10^i - 1)*10^zeros ] ]; high = Floor[ Sqrt[ (2/3*(10^i - 1) + 1)*10^zeros ] ]; isFound = (low <= high); zeros++ ]; Print[ low, " ", low^2 ] ]

%Y Cf. A034989.

%K nonn,base

%O 1,1

%A _Patrick De Geest_, Nov 15 1998

%E Program and more terms from Jonathan Cross (jcross(AT)wcox.com), Oct 15 2001