A155150 -id:A155150 - cp's OEIS frontend

A155148 Numbers k such that k^4 has exactly 2 different decimal digits.

2, 3, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 10000000000, 100000000000, 1000000000000, 10000000000000, 100000000000000, 1000000000000000, 10000000000000000, 100000000000000000, 1000000000000000000, 10000000000000000000, 100000000000000000000, 1000000000000000000000

Offset: 1

Dmitry Kamenetsky, Jan 21 2009

Cf. A155149, A155150

for n from 1 do convert(convert(n^4,base,10),set) ; if nops(%) = 2 then print(n) ; fi; od: # R. J. Mathar, Feb 08 2009

A155148_list, m = [], [24, -36, 14, -1, 0]
for n in range(1,10**6+1):
    for i in range(4):
        m[i+1] += m[i]
    if len(set(str(m[-1]))) == 2:
        A155148_list.append(n) # Chai Wah Wu, Nov 05 2014

Two more terms from R. J. Mathar, Feb 08 2009
a(9)-a(12) from Charles R Greathouse IV, Aug 01 2010
More terms from David A. Corneth, Jun 30 2025

A155149 Numbers k such that k^4 has exactly 3 different decimal digits.

Original entry on oeis.org

4, 5, 9, 11, 16, 20, 30, 34, 200, 300, 2000, 3000, 20000, 30000, 200000, 300000, 2000000, 3000000, 20000000, 30000000, 200000000, 300000000, 2000000000, 3000000000, 20000000000, 30000000000

Offset: 1

Dmitry Kamenetsky, Jan 21 2009

Are there any more terms not of the form k * 10^n for k in {2, 3}?

Cf. A155148, A155150.

A155149_list = [n for n in range(1,10**6) if len(set(str(n**4))) == 3]
# Chai Wah Wu, Sep 27 2014

Comment and more terms from Charles R Greathouse IV, Nov 12 2010
a(21)-a(22) from Chai Wah Wu, Sep 27 2014
a(23)-a(26) from Michael S. Branicky, Jun 28 2023

A247045 Triangle read by rows: T(n,k) = least number m > 0 such that m^k in base n contains exactly k distinct digits, 1 <= k <= n.

Original entry on oeis.org

1, 1, 2, 1, 3, 4, 1, 2, 3, 5, 1, 3, 3, 6, 12, 1, 3, 5, 7, 7, 15, 1, 3, 5, 9, 5, 17, 15, 1, 4, 5, 10, 9, 7, 11, 33, 1, 3, 5, 7, 11, 19, 14, 16, 53, 1, 4, 5, 6, 7, 13, 13, 14, 21, 36, 1, 4, 5, 7, 10, 8, 12, 12, 16, 42, 41, 1, 4, 6, 16, 11, 8, 19, 19, 16, 28, 35, 55, 1, 4, 6, 9, 9, 14, 10, 18, 14

Offset: 1

Derek Orr, Sep 10 2014

			T(n,k) is given by (row n corresponds to base n):
1;
1, 2;
1, 3, 4;
1, 2, 3,  5;
1, 3, 3,  6, 12;
1, 3, 5,  7,  7, 15;
1, 3, 5,  9,  5, 17, 15;
1, 4, 5, 10,  9,  7, 11, 33;
1, 3, 5,  7, 11, 19, 14, 16, 53;
1, 4, 5,  6,  7, 13, 13, 14, 21, 36; (base 10)
1, 4, 5,  7, 10,  8, 12, 12, 16, 42, 41;
Example: T(7,3) = 5 means that 5 is the smallest number such that 5^3 in base 7 (which is 125 in base 7 = 236) has 3 distinct digits (2, 3, and 6).

Indranil Ghosh, Rows 1..36 of triangle, flattened

Cf. A016069, A155146, A155150.

print1(1,", ");n=2;while(n<20,m=1;for(k=1,n,while(m,d=digits(m^k,n);if(#vecsort(d,,8)!=k,m++);if(#vecsort(d,,8)==k,print1(m,", ");m=1;break)));n++)

A247047 Numbers k such that k^2 contains exactly 2 distinct digits and k^3 contains exactly 3 distinct digits.

Original entry on oeis.org

5, 6, 8, 9, 15, 30, 173, 300, 3000, 30000, 300000, 3000000, 30000000, 300000000, 3000000000, 30000000000, 300000000000, 3000000000000, 30000000000000, 300000000000000, 3000000000000000

Offset: 1

Derek Orr, Sep 10 2014

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.)

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

Cf. A016069, A155146.

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 *)

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,", ")))

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

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

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A155148 Numbers k such that k^4 has exactly 2 different decimal digits.

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A155149 Numbers k such that k^4 has exactly 3 different decimal digits.

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A247045 Triangle read by rows: T(n,k) = least number m > 0 such that m^k in base n contains exactly k distinct digits, 1 <= k <= n.

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A247047 Numbers k such that k^2 contains exactly 2 distinct digits and k^3 contains exactly 3 distinct digits.

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