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

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.)

Links

Table of n, a(n) for n=1..18.

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

Cf. A016069, A155146.

Sequence in context: A308708 A125251 A271728 * A218866 A227760 A055592

Adjacent sequences: A247044 A247045 A247046 * A247048 A247049 A247050

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