A060712 Smallest number whose sum of digits is 3^n.

1, 3, 9, 999, 999999999, 999999999999999999999999999, 999999999999999999999999999999999999999999999999999999999999999999999999999999999

Offset: 0

Author

Robert G. Wilson v, Apr 21 2001

Keywords

• nonn
• base

Links

• Harry J. Smith, Table of n, a(n) for n = 0..8

Crossrefs

Cf. A051885.

Programs

Mathematica

Do[ a = {}; While[ Apply[ Plus, a ] + 9 < 3^n, a = Append[ a, 9 ] ]; If[ Apply[ Plus, a ] != 3^n, a = Prepend[ a, 3^n - Apply[ Plus, a ] ] ]; Print[ FromDigits[ a ] ], {n, 1, 6} ]
Join[{1,3},Table[FromDigits[PadRight[{},3^(n-2),9]],{n,2,6}]] (* Harvey P. Dale, Jun 10 2015 *)

PARI

a(n)={ my(s=3^n, x=s\9, d=s-9*x); (d+1)*10^x - 1 } \\ Harry J. Smith, Jul 10 2009

Formula

a(n) = A051885(3^n). - Andrew Howroyd, Dec 08 2024

a(n) = 10^(3^(n-2)) - 1 for n > 1. - Stefano Spezia, Mar 27 2025