cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A030295 Cubes with at most three distinct digits.

Original entry on oeis.org

0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 2744, 3375, 8000, 27000, 46656, 64000, 238328, 343000, 778688, 1000000, 1030301, 1331000, 5177717, 7077888, 8000000, 9393931, 27000000, 64000000, 343000000, 700227072
Offset: 1

Views

Author

Keywords

Crossrefs

Cf. A030293 (subsequence), A030294, A235718.

Programs

  • Mathematica
    Select[Range[900]^3, Length@ Union@ IntegerDigits[#] <= 3 &] (* Michael De Vlieger, Feb 10 2020 *)
  • PARI
    disdigs(n,nd)={my(v=vector(10),d=digits(n^3));for(j=1,#d,v[d[j]+1]=1);if(vecsum(v)<=nd,n^3,0)};
    print1(0,", ");for(k=1,1000,if(j=disdigs(k,3),print1(j,", "))) \\ Hugo Pfoertner, Feb 10 2020

Formula

a(n) = A030294(n)^3. - Peter Munn, Feb 02 2020

A202940 Positive numbers n such that n is not a multiple of 10 and n^3 has at most three different digits.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 14, 15, 36, 62, 92, 101, 173, 192, 211, 888, 1001, 3543, 10001, 100001, 110011, 146796, 1000001, 10000001, 100000001
Offset: 1

Views

Author

Zak Seidov, Dec 26 2011

Keywords

Comments

Subsequence of A030294 where trailing zeros are allowed.
Conjecture: no more terms other than those of the form 10^n+1, n=0,1,2,... .

Crossrefs

Cf. A030294.

Programs

  • Mathematica
    Select[Range[150000],Mod[#,10]!=0&&Count[DigitCount[#^3],0]>6&] (* The program generates the first 26 terms of the sequience. To generate more, increase the Range constant but the program may take a long time to run. *) (* Harvey P. Dale, Sep 04 2021 *)
  • PARI
    for(n=1,10^9+1, if((n%10!=0) && #Set(digits(n^3))<=3, print1(n,", ")));
    \\ Joerg Arndt, Dec 13 2014

A308708 Numbers k such that k^3 contains exactly three distinct digits; numbers with trailing zeros are excluded.

Original entry on oeis.org

5, 6, 8, 9, 14, 15, 36, 62, 92, 101, 173, 192, 211, 888, 1001, 3543, 10001, 100001, 110011, 146796, 1000001, 10000001, 100000001, 1000000001, 10000000001
Offset: 1

Views

Author

Andrej Jakobcic, Aug 01 2019

Keywords

Comments

10^k + 1 (A000533(k)) is a term for k >= 2. - Jinyuan Wang, Aug 02 2019

Examples

			a(8) = 62 because 62^3 = 238328, which contains exactly three distinct digits.
		

Crossrefs

Programs

  • Magma
    [k:k in [1..10000001]| k mod 10 ne 0 and  #Set(Intseq(k^3)) eq 3]; // Marius A. Burtea, Aug 02 2019
  • Mathematica
    Select[Range[10001], Mod[#, 10] > 0 && Length@ Union@ IntegerDigits[#^3] == 3 &] (* Giovanni Resta, Sep 05 2019 *)
  • PARI
    is(k) = #vecsort(digits(k^3), , 8)==3 && k%10!=0; \\ Jinyuan Wang, Aug 02 2019
    

Extensions

More terms from Jinyuan Wang, Aug 02 2019
a(23)-a(25) from Jon E. Schoenfield, Aug 02 2019

A385175 Cubes using at most three distinct digits, not ending in 0.

Original entry on oeis.org

1, 8, 27, 64, 125, 216, 343, 512, 729, 1331, 2744, 3375, 46656, 238328, 778688, 1030301, 5177717, 7077888, 9393931, 700227072, 1003003001, 44474744007, 1000300030001, 1000030000300001, 1331399339931331, 3163316636166336, 1000003000003000001, 1000000300000030000001, 1000000030000000300000001
Offset: 1

Views

Author

Gonzalo Martínez, Jun 20 2025

Keywords

Comments

This sequence has infinitely many terms since (10^m + 1)^3 is a term for all m >= 0.
Conjecture: a(26) = 3163316636166336 is the largest term with nonzero digits (See comments of A030294 and the data of A155146, where a(26) = A155146(47)^3).

Examples

			8, 343, and 46656 belong to this list because they are cubes that use 1, 2, and 3 distinct digits, respectively.
		

Crossrefs

Programs

  • Mathematica
    Select[Range[10^6]^3,Length[Union[IntegerDigits[#]]]<4&&IntegerDigits[#][[-1]]!=0&] (* James C. McMahon, Jun 30 2025 *)
    fQ[n_] := Mod[n, 10] > 0 && Length@ Union@ IntegerDigits[n^3] < 4; k = 1; lst = {}; While[k < 1000002, If[ fQ@k, AppendTo[lst, k]]; k++]; lst^3 (* Robert G. Wilson v, Jul 10 2025 *)

Formula

a(n) = A202940(n)^3.

Extensions

a(28) from Robert G. Wilson v, Jul 10 2025
a(29) from David A. Corneth, Jul 10 2025
Showing 1-4 of 4 results.