A155150 Numbers k such that k^4 has exactly 4 distinct decimal digits.

6, 7, 8, 15, 19, 21, 24, 27, 28, 36, 39, 40, 42, 46, 50, 52, 57, 64, 67, 69, 70, 80, 85, 88, 90, 101, 110, 131, 150, 160, 183, 190, 202, 203, 340, 400, 433, 500, 570, 670, 700, 800, 843, 850, 900, 1001, 1010, 1100, 1171, 1500, 1600, 1900, 2673, 2868, 3400, 4000

Offset: 1

Author

Dmitry Kamenetsky, Jan 21 2009

Keywords

• nonn
• base

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A155148, A155149

Programs

Magma

[n: n in [0..4000] | #Set(Intseq(n^4)) eq 4]; // Vincenzo Librandi, Nov 07 2014

Mathematica

ddd4Q[n_]:=Count[DigitCount[n^4],?(#>0&)]==4; Select[Range[5000],ddd4Q] (* _Harvey P. Dale, Nov 10 2012 *)
Select[Range[4000], Length[Union[IntegerDigits[#^4]]]==4&] (* Vincenzo Librandi, Nov 07 2014 *)

Python

A155150_list, m = [], [24, -36, 14, -1, 0]
for n in range(1, 10**3+1):
    for i in range(4):
        m[i+1] += m[i]
    if len(set(str(m[-1]))) == 4:
        A155150_list.append(n) # Chai Wah Wu, Nov 05 2014

Extensions

Edited by Charles R Greathouse IV, Aug 02 2010