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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

%I #22 Jan 21 2023 13:58:10

%S 5,6,8,9,15,30,173,300,3000,30000,300000,3000000,30000000,300000000,

%T 3000000000,30000000000,300000000000,3000000000000

%N Numbers k such that k^2 contains exactly 2 distinct digits and k^3 contains exactly 3 distinct digits.

%C Intersection of A016069 and A155146.

%C This sequence is infinite since 3*10^k is always in this sequence for k > 0.

%C Is 173 the last term not of the form 3*10^k?

%C 3*10^7 < a(14) <= 3*10^8.

%C 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.)

%e k = 15 is a member of this sequence since 15^2 = 225 contains two distinct digits and 15^3 = 3375 contains three distinct digits.

%t 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 *)

%o (PARI)

%o 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,", ")))

%o (Python)

%o A247047_list = [n for n in range(1,10**6) if len(set(str(n**3))) == 3 and len(set(str(n**2))) == 2]

%o # _Chai Wah Wu_, Sep 26 2014

%Y Cf. A016069, A155146.

%K nonn,base,more

%O 1,1

%A _Derek Orr_, Sep 10 2014

%E a(14)-a(15) from _Chai Wah Wu_, Sep 26 2014

%E a(16)-a(18) from _Kevin P. Thompson_, Jul 01 2022

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Last modified March 29 05:28 EDT 2024. Contains 371264 sequences. (Running on oeis4.)