A178983 The smallest cube containing n as a substring.

0, 1, 27, 343, 64, 125, 64, 27, 8, 729, 1000, 91125, 125, 1331, 140608, 15625, 216, 1728, 85184, 2197, 205379, 216, 226981, 103823, 13824, 125, 9261, 27, 1728, 729, 39304, 1331, 5832, 1331, 343, 35937, 97336, 3375, 13824, 39304, 4096, 531441, 42875, 343

Offset: 0

Author

Andy Martin, Jan 02 2011

Keywords

• nonn
• easy
• base

Examples

			a(3) = 7^3 = 343, because it contains 3 as a substring and no smaller cube contains 3.
		

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A029943, A029947.

Programs

Mathematica

subs[n_] := Module[{d = IntegerDigits[n], len}, len = Length[d]; Union[Flatten[Table[FromDigits[Take[d, {i, k}]], {k, len}, {i, k}]]]]; Table[k = 0; While[! MemberQ[subs[k^3], n], k++]; k^3, {n, 0, 100}] (* T. D. Noe, Nov 06 2013 *)
With[{cbs=Range[0,100]^3},Table[SelectFirst[cbs,SequenceCount[IntegerDigits[#],IntegerDigits[n]]>0&],{n,0,50}]] (* Harvey P. Dale, Nov 17 2024 *)

Ruby

# For a given nonnegative integer n,
# find the smallest nonnegative cube that contains it as a substring.
NUM_TERMS = 30
(0...NUM_TERMS).each{ |i|
  (0..(1.0/0.0)).each{ |j|
    (print "#{j*j*j}" + ", "; break) if "#{j*j*j}".include?("#{i}")
  }
}

Extensions

Edited by Alois P. Heinz, Jan 02 2011