A030673 - OEIS

%I #14 Jul 18 2014 08:33:19

%S 27,343,512,729,110592,1331,1728,19683,238328,29791,314432,373248,

%T 4173281,438976,474552,531441,59319,614125,6751269,7189057,7301384,

%U 79507,830584,8998912,97336,101194696,103823,10793861,1092727,11390625

%N Smallest cube that begins with n-th prime.

%H Robert G. Wilson v, <a href="/A030673/b030673.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A018797(A000040(n)).

%e a(1) = 27 because 27 = 3^3 is the smallest cube beginning (base 10) with prime(1) = 2.

%e a(2) = 343 because 343 = 7^3 is the smallest cube beginning (base 10) with prime(2) = 3.

%t f[n_] := Block[{k, l = Ceiling@ Log[10, Prime@ n], p = IntegerDigits@ Prime@ n}, k = Ceiling[ Prime[n]^(1/3)]; While[ Take[ IntegerDigits[k^3], l] != p, k++ ]; k^3]; Array[f, 31] (* _Robert G. Wilson v_, May 31 2008 *)

%Y Cf. A000040, A000578, A018797, A030674.

%K base,easy,nonn

%O 1,1

%A _Patrick De Geest_

%E Edited by _N. J. A. Sloane_, Aug 29 2008 at the suggestion of _R. J. Mathar_