A030673 Smallest cube that begins with n-th prime.

27, 343, 512, 729, 110592, 1331, 1728, 19683, 238328, 29791, 314432, 373248, 4173281, 438976, 474552, 531441, 59319, 614125, 6751269, 7189057, 7301384, 79507, 830584, 8998912, 97336, 101194696, 103823, 10793861, 1092727, 11390625

Offset: 1

Author

Patrick De Geest

Keywords

• base
• easy
• nonn

Examples

			a(1) = 27 because 27 = 3^3 is the smallest cube beginning (base 10) with prime(1) = 2.
a(2) = 343 because 343 = 7^3 is the smallest cube beginning (base 10) with prime(2) = 3.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A000578, A018797, A030674.

Programs

Mathematica

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 *)

Formula

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

Extensions

Edited by N. J. A. Sloane, Aug 29 2008 at the suggestion of R. J. Mathar