A060711 Smallest number whose sum of digits is n^4.

1, 79, 999999999, 49999999999999999999999999999, 4999999999999999999999999999999999999999999999999999999999999999999999, 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

Offset: 1

Author

Robert G. Wilson v, Apr 21 2001

Keywords

• nonn
• base

Links

• Harry J. Smith, Table of n, a(n) for n = 1..9

Crossrefs

Cf. A051885, A061104, A061105.

Programs

Mathematica

Do[ a = {}; While[ Apply[ Plus, a ] + 9 < n^4, a = Append[ a, 9 ] ]; If[ Apply[ Plus, a ] != n^4, a = Prepend[ a, n^4 - Apply[ Plus, a ] ] ]; Print[ FromDigits[ a ] ], {n, 1, 6} ]

PARI

a(n)={ my(s=n^4, x=s\9, d=s-9*x); (d+1)*10^x - 1 } \\ Harry J. Smith, Jul 10 2009

Formula

a(n) = A051885(n^4).

a(n) >= 10^(n^4/9) - 1.