A247047 Numbers k such that k^2 contains exactly 2 distinct digits and k^3 contains exactly 3 distinct digits.
5, 6, 8, 9, 15, 30, 173, 300, 3000, 30000, 300000, 3000000, 30000000, 300000000, 3000000000, 30000000000, 300000000000, 3000000000000, 30000000000000, 300000000000000, 3000000000000000
Offset: 1
Examples
k = 15 is a member of this sequence since 15^2 = 225 contains two distinct digits and 15^3 = 3375 contains three distinct digits.
Programs
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Mathematica
Select[Range[3*10^6],Length[DeleteCases[DigitCount[#^2],0]]==2&&Length[ DeleteCases[ DigitCount[#^3],0]]==3&] (* The program generates the first 12 terms of the sequence. *) (* Harvey P. Dale, Jan 21 2023 *)
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PARI
for(n=1,3*10^7,d2=digits(n^2);d3=digits(n^3);if(#vecsort(d2,,8)==2&vecsort(d3,,8)==3,print1(n,", ")))
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Python
A247047_list = [n for n in range(1,10**6) if len(set(str(n**3))) == 3 and len(set(str(n**2))) == 2] # Chai Wah Wu, Sep 26 2014
Extensions
a(14)-a(15) from Chai Wah Wu, Sep 26 2014
a(16)-a(18) from Kevin P. Thompson, Jul 01 2022
a(19)-a(21) from Michael S. Branicky, Jun 05 2025
Comments