A067103 a(n) = floor(X/Y), where X = concatenation of cubes and Y = concatenation of natural numbers.

1, 1, 14, 148, 14804, 1480398, 148039049, 14803895356, 1480389427723, 148038942652481, 14803894265116205, 1480389426511476635, 148038942651147507639, 14803894265114750596056, 1480389426511475059425814, 148038942651147505942389607, 14803894265114750594238756940

Offset: 1

Author

Robert G. Wilson v, Jan 09 2002

Keywords

• nonn
• base

Comments

a(n) -> 148038942651147505942387547594667814093751032610233441970375...

Examples

			a(6) = floor(182764125216/123456) = floor(1480398.888802...) = 1480398.
		

Crossrefs

Cf. A000578, A007908, A019522.

Cf. A067091, A067092, A067093, A067094, A067095, A067096, A067097, A067098, A067099, A067100, A067101, A067102.

See also A066700.

Programs

Maple

a:= n-> floor(parse(cat(i^3$i=1..n))/parse(cat($1..n))):
seq(a(n), n=1..17);  # Alois P. Heinz, May 25 2022

Mathematica

f[n_] := (k = 1; x = y = "0"; While[k < n + 1, x = StringJoin[x, ToString[k^3]]; y = StringJoin[y, ToString[k]]; k++ ]; Return[ Floor[ ToExpression[x] / ToExpression[y]]] ); Table[ f[n], {n, 1, 20} ]
nn=20;With[{c=Table[IntegerDigits[n^3],{n,nn}],s=Table[IntegerDigits[n],{n,nn}]}, Table[Floor[FromDigits[Flatten[Take[c,i]]]/FromDigits[Flatten[Take[s,i]]]],{i,nn}]] (* Harvey P. Dale, Feb 10 2013 *)

PARI

c1(n) = my(s=""); for(k=1, n, s=Str(s, k)); eval(s); \\ A007908
c3(n) = my(s=""); for(k=1, n, s=Str(s, k^3)); eval(s); \\ A019522
a(n) = c3(n)\c1(n); \\ Michel Marcus, May 25 2022