A074100 Cubes using only digits 1, 2, 3, 5 and 7.

1, 27, 125, 512, 1331, 3375, 753571, 2571353, 5177717, 17173512, 25153757, 72511713, 11512557512, 22211737731, 27135225125, 125375375125, 552377215125, 2252212155712, 3531251132352, 7127771131125, 23771111713777, 31122112521375, 37521355131352, 125112533753375

Offset

1,2

Comments

Conjecture: the sequence is finite.

Opposite conjecture: the sequence is infinite. The frequency of terms with k digits is 4, 3, 5, 5, 9, 11, 12, 13, 22, 29, 33, 37, 49, 49, 78 for k = 1..15 respectively. - David A. Corneth, Mar 17 2019

Links

David A. Corneth, Table of n, a(n) for n = 1..359 (Terms < 10^45; first 37 terms from Jayanta Basu)

Example

137^3 = 2571353, smallest term using the five digits 1, 2, 3, 5 and 7. - Bernard Schott, Mar 18 2019
91^3 = 753571 as 753571 uses only digits from 1, 2, 3, 5 and 7. It's fine that 91 doesn't. - David A. Corneth, Mar 18 2019

Mathematica

t1 = Prepend[Prime[Range[4]], 1]; Select[Range[35000]^3, Complement[IntegerDigits[#], t1] == {} &] (* Jayanta Basu, Jul 31 2013 *)

Prog

(Python)
A074100_list = [n**3 for n in range(1, 10**6) if set(str(n**3)) <= set('12357')] # Chai Wah Wu, Mar 16 2019

Crossrefs

Cf. A079656.

Sequence in context: A371189 A126272 A016755 * A082610 A061434 A092770

Adjacent sequences: A074097 A074098 A074099 * A074101 A074102 A074103

Keyword

nonn,base

Author

Amarnath Murthy, Aug 21 2002

Extensions

More terms from Sascha Kurz, Jan 30 2003

Two more terms from Jayanta Basu, Jul 31 2013

Status

approved