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A247047
Numbers k such that k^2 contains exactly 2 distinct digits and k^3 contains exactly 3 distinct digits.
0
5, 6, 8, 9, 15, 30, 173, 300, 3000, 30000, 300000, 3000000, 30000000, 300000000, 3000000000, 30000000000, 300000000000, 3000000000000
OFFSET
1,1
COMMENTS
Intersection of A016069 and A155146.
This sequence is infinite since 3*10^k is always in this sequence for k > 0.
Is 173 the last term not of the form 3*10^k?
3*10^7 < a(14) <= 3*10^8.
The numbers k such that k^2 contains 2 distinct digits, k^3 contains 3 distinct digits, and k^4 contains 4 distinct digits are conjectured to only be 6, 8, and 15. (Intersection of A016069, A155146, and A155150.)
EXAMPLE
k = 15 is a member of this sequence since 15^2 = 225 contains two distinct digits and 15^3 = 3375 contains three distinct digits.
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 *)
PROG
(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, ", ")))
(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
CROSSREFS
Sequence in context: A308708 A125251 A271728 * A218866 A227760 A055592
KEYWORD
nonn,base,more
AUTHOR
Derek Orr, Sep 10 2014
EXTENSIONS
a(14)-a(15) from Chai Wah Wu, Sep 26 2014
a(16)-a(18) from Kevin P. Thompson, Jul 01 2022
STATUS
approved