A052048 Cubes whose digits occur with the same frequency.

0, 1, 8, 27, 64, 125, 216, 512, 729, 1331, 1728, 2197, 4096, 4913, 5832, 6859, 9261, 10648, 13824, 19683, 24389, 32768, 42875, 54872, 68921, 205379, 238328, 287496, 328509, 389017, 421875, 438976, 592704, 681472, 804357, 912673, 2460375, 3048625

Offset: 1

Author

Patrick De Geest, Dec 15 1999

Keywords

• nonn
• base

Examples

			E.g., 238328 = 62^3 -> digits 2, 3 and 8 occur each twice.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..450
• Patrick De Geest, Numbers whose digits occur with same frequency

Crossrefs

Cf. A052047, A045540, A052046, A052049, A052050, A052051, A052052.

Programs

Maple

isA052048 := proc(n) local d,k,fr,eqfr: if(n=0)then return true: fi: d:=convert(n^3,base,10): eqfr:=true: fr:=numboccur(d[1],d): for k from 0 to 9 do if(not member(numboccur(k,d),{fr,0}))then eqfr:=false: break: fi: od: return eqfr: end: seq(`if`(isA052048(n), n^3, NULL), n=0..200); # Nathaniel Johnston, May 31 2011

Mathematica

t={}; Do[If[Length[DeleteDuplicates[Transpose[Tally[IntegerDigits[n^3]]][[2]]]]==1,AppendTo[t,n^3]],{n,0,200}]; t (* Jayanta Basu, May 11 2013 *)

Formula

a(n) = A052047(n)^3. - Andrew Howroyd, Aug 11 2024

Extensions

Offset corrected by Andrew Howroyd, Aug 11 2024