A061434 a(n) is the smallest n-digit cube.

1, 27, 125, 1000, 10648, 103823, 1000000, 10077696, 100544625, 1000000000, 10007873875, 100026577288, 1000000000000, 10000909453625, 100000721719296, 1000000000000000, 10000073940248384, 100000075387171679, 1000000000000000000, 10000004316234262875

Offset: 1

Author

Amarnath Murthy, May 03 2001

Keywords

• nonn
• base
• easy

Examples

			a(4) = 1000 = 10^3 has 4 digits while 9^3 = 729 has 3 digits.
		

Crossrefs

Cf. A000578, A061432, A061433.

Programs

Maple

A061434 := n->ceil(10^((n-1)/3))^3;

Mathematica

Table[Ceiling[Surd[10^n,3]]^3,{n,0,20}] (* Harvey P. Dale, Oct 09 2023 *)

PARI

a(n) = ceil(10^((n-1)/3))^3; \\ Michel Marcus, Jan 27 2021

Python

from sympy import integer_nthroot
def a(n):
  r, exact = integer_nthroot(10**(n-1), 3)
  return 10**(n-1) if exact else (r+1)**3
print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Jan 27 2021

Formula

a(n) = ceiling(10^((n-1)/3))^3. - Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 30 2003

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 16 2001

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 30 2003