A018797 Smallest cube that begins with n.

0, 1, 27, 343, 4096, 512, 64, 729, 8, 9261, 1000, 110592, 125, 1331, 140608, 15625, 166375, 1728, 185193, 19683, 205379, 216, 226981, 238328, 24389, 250047, 262144, 27, 287496, 29791, 300763, 314432, 32768, 3375, 343, 35937, 3652264, 373248

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• base
• nice

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 1..1000 from T. D. Noe)

Crossrefs

Cf. A018852, A018796.

Programs

Mathematica

a[n_] := For[idn = IntegerDigits[n]; k = 1, True, k++, idk = IntegerDigits[k^3]; If[Length[idn] <= Length[idk], If[idk[[1 ;; Length[idn]]] == idn, Return[k^3]]]]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 1000}] (* Jean-François Alcover, Mar 13 2016 *)
id[n_]:=With[{idn=IntegerDigits[n]},idn==Take[IntegerDigits[#], Length[ idn]]&]; With[{c=Range[0,250]^3},Table[SelectFirst[c,id[k]],{k,0,40}]]//Quiet (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 08 2018 *)

Python

for n in range(1, 10**3):
  for k in range(10**3):
    if str(k**3).startswith(str(n)):
      print(k**3, end=', ')
      break
  n += 1 # Derek Orr, Aug 03 2014

Formula

a(n) = A018852(n)^3. - Seiichi Manyama, Jan 30 2017

Extensions

Added initial 0. - Seiichi Manyama, Jan 30 2017