A061105 Smallest number whose digital sum is n^3.

0, 1, 8, 999, 19999999, 89999999999999, 999999999999999999999999, 199999999999999999999999999999999999999, 899999999999999999999999999999999999999999999999999999999

Offset

0,3

Comments

Except for the leading digit all the other digits of a(n), n >= 1, are 9's and the leading digit is 1 or 8. (This is because the digital sum of n^3 is congruent to 0, 1, or 8 mod 9, so the best we can do is use as many 9's as possible, prefixed if necessary by 1 or 8. - N. J. A. Sloane, Jul 19 2018)

Links

Harry J. Smith, Table of n, a(n) for n=0,...,20

Formula

a(n) =((n mod 3)^3+1)*10^floor[n^3/9]-1 =(A021559(n+1)+1)*10^A061263(n)-1. - Henry Bottomley, Apr 24 2001

Example

a(4) = 19999999, 1+9+9+9+9+9+9+9 = 64 = 4^3.

Mathematica

Do[a = {}; While[Apply[Plus, a] + 9 < n^3, a = Append[a, 9]]; If[ Apply[ Plus, a] != n^3, a = Prepend[ a, n^3 - Apply[ Plus, a]] ]; Print[ FromDigits[ a]], {n, 1, 10} ]
dsn3[n_]:=Module[{t=(n^3-{0, 1, 8})/9}, Which[ IntegerQ[t[[1]]], FromDigits[ PadRight[ {}, t[[1]], 9]], IntegerQ[t[[2]]], FromDigits[ PadRight[ {1}, t[[2]]+1, 9]], IntegerQ[t[[3]]], FromDigits[PadRight[{8}, t[[3]]+1, 9]]]]; Array[dsn3, 10, 0] (* Harvey P. Dale, Jul 19 2018 *)

Prog

(PARI) { for (n=0, 20, a=((n%3)^3 + 1)*10^(n^3\9) - 1; write("b061105.txt", n, " ", a) ) } \\ Harry J. Smith, Jul 19 2009

Crossrefs

Cf. A061104.

Sequence in context: A183888 A181965 A159868 * A118545 A017091 A164883

Adjacent sequences: A061102 A061103 A061104 * A061106 A061107 A061108

Keyword

nonn,base

Author

Amarnath Murthy, Apr 20 2001

Extensions

More terms from Robert G. Wilson v, Apr 21 2001

Status

approved