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A235808 Numbers k such that k^3 has one or more occurrences of exactly six different digits.

%I A235808 #22 Jun 12 2025 16:49:46
%S A235808 59,66,69,73,75,76,84,88,93,97,107,112,113,115,116,118,124,128,129,
%T A235808 131,139,147,148,151,156,159,161,166,168,169,174,178,181,183,184,187,
%U A235808 189,193,194,196,207,219,226,232,234,235,236,238,240,241,246,253,255,262
%N A235808 Numbers k such that k^3 has one or more occurrences of exactly six different digits.
%H A235808 Colin Barker, <a href="/A235808/b235808.txt">Table of n, a(n) for n = 1..1000</a>
%e A235808 59 is in the sequence because 59^3 = 205379, which contains exactly six different digits: 0, 2, 3, 5, 7, 9.
%e A235808 107 is in the sequence because 107^3 = 1225043, which contains exactly six different digits: 0, 1, 2, 3, 4, 5.
%t A235808 Select[Range[300], Length[Union[IntegerDigits[#^3]]] == 6 &] (* _Bruno Berselli_, Jan 19 2014 *)
%t A235808 Select[Range[300],Count[DigitCount[#^3],0]==4&] (* _Harvey P. Dale_, May 28 2025 *)
%o A235808 (PARI) s=[]; for(n=1, 300, if(#vecsort(eval(Vec(Str(n^3))),,8)==6, s=concat(s, n))); s
%o A235808 (Magma) [n: n in [0..300] | #Set(Intseq(n^3)) eq 6]; // _Bruno Berselli_, Jan 19 2014
%o A235808 (Python)
%o A235808 A235808_list, m = [], [6, -6, 1, 0]
%o A235808 for n in range(1,10**4+1):
%o A235808     for i in range(3):
%o A235808         m[i+1] += m[i]
%o A235808     if len(set(str(m[-1]))) == 6:
%o A235808         A235808_list.append(n) # _Chai Wah Wu_, Nov 05 2014
%Y A235808 Cf. A030292, A155146, A155147, A235807, A235809-A235811, A119735.
%K A235808 nonn,base
%O A235808 1,1
%A A235808 _Colin Barker_, Jan 19 2014