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 1-8 of 8 results.

A119735 Numbers n such that every digit occurs at least once in n^3.

Original entry on oeis.org

2326, 2535, 2795, 3123, 3506, 3909, 4602, 4782, 5027, 5048, 5196, 5362, 5394, 5402, 5437, 6215, 6221, 6517, 6687, 6789, 6802, 6993, 7061, 7202, 7219, 7616, 7638, 8124, 8244, 8248, 8288, 8384, 8402, 8443, 8496, 8499, 8817, 9006, 9048, 9142, 9374, 9476
Offset: 1

Views

Author

Dmitry Kamenetsky, Jun 15 2006

Keywords

Links

Crossrefs

Cf. A030292.

Programs

  • Mathematica
    Select[Range[10000],Union[IntegerDigits[#^3]]==Range[0,9]&] (* Harvey P. Dale, Apr 11 2014 *)
  • PARI
    isok(n) = length(Set(digits(n^3))) == 10; \\ Michel Marcus, Aug 28 2013
  • Python
    A119735_list, m = [], [6, -6, 1, 0]
for n in range(1,10**6+1):
    for i in range(3):
        m[i+1] += m[i]
    if len(set(str(m[-1]))) == 10:
        A119735_list.append(n) # Chai Wah Wu, Nov 05 2014

A155146 Numbers k such that k^3 has exactly 3 different digits.

Original entry on oeis.org

5, 6, 8, 9, 14, 15, 30, 36, 40, 62, 70, 92, 101, 110, 173, 192, 211, 300, 400, 700, 888, 1001, 1010, 1100, 1920, 3000, 3543, 4000, 7000, 8880, 10001, 10010, 10100, 11000, 19200, 30000, 35430, 40000, 70000, 88800, 100001, 100010, 100100, 101000, 110000, 110011
Offset: 1

Views

Author

Dmitry Kamenetsky, Jan 21 2009

Keywords

Examples

			14 is in the list because 14^3 = 2744. - _Jon Perry_, Nov 04 2014

Links

Crossrefs

Cf. A030292.

Programs

  • Magma
    [n: n in [0..120000] | #Set(Intseq(n^3)) eq 3]; // Vincenzo Librandi, Nov 04 2014
  • Maple
    a := proc (n) if nops(convert(convert(n^3, base, 10), set)) = 3 then n else end if end proc: seq(a(n), n = 1 .. 150000); # Emeric Deutsch, Jan 27 2009
  • Mathematica
    Select[Range[120000], Length[Union[IntegerDigits[#^3]]]==3&] (* Vincenzo Librandi, Nov 04 2014 *)
  • PARI
    is(n)=#Set(digits(n^3))==3 \\ Charles R Greathouse IV, Feb 11 2017
  • Python
    A155146_list, n3, m = [], 0, 0
for n in range(1,10**7):
    m += 6*(n-1)
    n3 += m + 1
    if len(set(str(n3))) == 3:
        A155146_list.append(n) # Chai Wah Wu, Nov 03 2014

Extensions

Extended by Emeric Deutsch, Jan 27 2009

A235807 Numbers n such that n^3 has one or more occurrences of exactly five different digits.

Original entry on oeis.org

22, 24, 27, 29, 32, 35, 38, 41, 47, 48, 49, 51, 52, 54, 55, 57, 61, 63, 65, 71, 72, 82, 85, 87, 89, 94, 96, 102, 103, 104, 105, 108, 109, 119, 120, 123, 125, 126, 127, 130, 133, 134, 136, 137, 138, 141, 143, 144, 149, 152, 153, 154, 155, 158, 162, 165, 167
Offset: 1

Views

Author

Colin Barker, Jan 19 2014

Keywords

Examples

			22 is in the sequence because 22^3 = 10648, which contains exactly five different digits: 0, 1, 4, 6, 8.
87 is in the sequence because 87^3 = 658503, which contains exactly five different digits: 0, 3, 5, 6, 8.

Links

Crossrefs

Cf. A030292, A155146, A155147, A235808-A235811, A119735.

Programs

  • Magma
    [n: n in [0..200] | #Set(Intseq(n^3)) eq 5]; // Bruno Berselli, Jan 19 2014
  • Mathematica
    Select[Range[200], Length[Union[IntegerDigits[#^3]]] == 5 &] (* Bruno Berselli, Jan 19 2014 *)
  • PARI
    s=[]; for(n=1, 200, if(#vecsort(eval(Vec(Str(n^3))),,8)==5, s=concat(s, n))); s
  • Python
    A235807_list, m = [], [6, -6, 1, 0]
for n in range(1,10**5+1):
    for i in range(3):
        m[i+1] += m[i]
    if len(set(str(m[-1]))) == 5:
        A235807_list.append(n) # Chai Wah Wu, Nov 05 2014

A235811 Numbers n such that n^3 has one or more occurrences of exactly nine different digits.

Original entry on oeis.org

1018, 1028, 1112, 1452, 1475, 1484, 1531, 1706, 1721, 1733, 1818, 1844, 1895, 1903, 2008, 2033, 2208, 2214, 2217, 2223, 2257, 2274, 2277, 2327, 2329, 2336, 2354, 2394, 2403, 2524, 2525, 2589, 2647, 2686, 2691, 2694, 2727, 2733, 2784, 2842, 2866, 2884, 2890
Offset: 1

Views

Author

Colin Barker, Jan 19 2014

Keywords

Examples

			1018 is in the sequence because 1018^3 = 1054977832, which contains exactly nine different digits.

Links

Crossrefs

Cf. A030292, A155146, A155147, A235807-A235810, A119735.

Programs

  • Mathematica
    Select[Range[3000],Count[DigitCount[#^3],0]==1&] (* Harvey P. Dale, Dec 17 2021 *)
  • PARI
    s=[]; for(n=1, 3000, if(#vecsort(eval(Vec(Str(n^3))),,8)==9, s=concat(s, n))); s
  • Python
    A235811_list, m = [], [6, -6, 1, 0]
for n in range(1,10**4+1):
    for i in range(3):
        m[i+1] += m[i]
    if len(set(str(m[-1]))) == 9:
        A235811_list.append(n) # Chai Wah Wu, Nov 05 2014

A235808 Numbers k such that k^3 has one or more occurrences of exactly six different digits.

Original entry on oeis.org

59, 66, 69, 73, 75, 76, 84, 88, 93, 97, 107, 112, 113, 115, 116, 118, 124, 128, 129, 131, 139, 147, 148, 151, 156, 159, 161, 166, 168, 169, 174, 178, 181, 183, 184, 187, 189, 193, 194, 196, 207, 219, 226, 232, 234, 235, 236, 238, 240, 241, 246, 253, 255, 262
Offset: 1

Views

Author

Colin Barker, Jan 19 2014

Keywords

Examples

			59 is in the sequence because 59^3 = 205379, which contains exactly six different digits: 0, 2, 3, 5, 7, 9.
107 is in the sequence because 107^3 = 1225043, which contains exactly six different digits: 0, 1, 2, 3, 4, 5.

Links

Crossrefs

Cf. A030292, A155146, A155147, A235807, A235809-A235811, A119735.

Programs

  • Magma
    [n: n in [0..300] | #Set(Intseq(n^3)) eq 6]; // Bruno Berselli, Jan 19 2014
  • Mathematica
    Select[Range[300], Length[Union[IntegerDigits[#^3]]] == 6 &] (* Bruno Berselli, Jan 19 2014 *)
Select[Range[300],Count[DigitCount[#^3],0]==4&] (* Harvey P. Dale, May 28 2025 *)
  • PARI
    s=[]; for(n=1, 300, if(#vecsort(eval(Vec(Str(n^3))),,8)==6, s=concat(s, n))); s
  • Python
    A235808_list, m = [], [6, -6, 1, 0]
for n in range(1,10**4+1):
    for i in range(3):
        m[i+1] += m[i]
    if len(set(str(m[-1]))) == 6:
        A235808_list.append(n) # Chai Wah Wu, Nov 05 2014

A235809 Numbers k such that k^3 has one or more occurrences of exactly seven different digits.

Original entry on oeis.org

135, 145, 203, 221, 223, 225, 227, 233, 243, 244, 245, 247, 249, 254, 257, 265, 272, 273, 275, 276, 299, 313, 327, 329, 334, 338, 341, 345, 347, 352, 365, 366, 368, 382, 384, 388, 393, 395, 398, 403, 405, 409, 411, 412, 434, 439, 447, 452, 455, 473, 486, 493
Offset: 1

Views

Author

Colin Barker, Jan 19 2014

Keywords

Examples

			135 is in the sequence because 135^3 = 2460375, which contains exactly seven different digits.

Links

Crossrefs

Cf. A030292, A155146, A155147, A235807, A235808, A235810, A235811, A119735.

Programs

  • Magma
    [n: n in [0..1200] | #Set(Intseq(n^3)) eq 7]; // Vincenzo Librandi, Nov 07 2014
  • Mathematica
    Select[Range[500], Length[Union[IntegerDigits[#^3]]]==7&] (* Vincenzo Librandi, Nov 07 2014 *)
  • PARI
    s=[]; for(n=1, 600, if(#vecsort(eval(Vec(Str(n^3))),,8)==7, s=concat(s, n))); s
  • PARI
    for(n=0,10^3,if(#Set(digits(n^3))==7,print1(n,", "))); \\ Joerg Arndt, Nov 10 2014
  • Python
    from itertools import count, islice
def A235809gen(): return filter(lambda n:len(set(str(n**3))) == 7,count(0))
A235809_list = list(islice(A235809gen(),26)) # Chai Wah Wu, Dec 23 2021

A235810 Numbers n such that n^3 has one or more occurrences of exactly eight different digits.

Original entry on oeis.org

289, 297, 302, 319, 467, 494, 515, 557, 562, 595, 621, 623, 676, 682, 709, 712, 721, 862, 887, 909, 939, 945, 949, 963, 984, 987, 1012, 1015, 1016, 1025, 1029, 1043, 1049, 1065, 1075, 1087, 1104, 1106, 1107, 1114, 1118, 1132, 1137, 1154, 1161, 1167, 1178
Offset: 1

Views

Author

Colin Barker, Jan 19 2014

Keywords

Examples

			289 is in the sequence because 289^3 = 24137569, which contains exactly eight different digits.

Links

Crossrefs

Cf. A030292, A155146, A155147, A235807-A235809, A235811, A119735.

Programs

  • Magma
    [n: n in [0..1200] | #Set(Intseq(n^3)) eq 8]; // Vincenzo Librandi, Nov 07 2014
  • PARI
    s=[]; for(n=1, 1500, if(#vecsort(eval(Vec(Str(n^3))),,8)==8, s=concat(s, n))); s
  • Python
    A235810_list, m = [], [6, -6, 1, 0]
for n in range(1,10**3+1):
    for i in range(3):
        m[i+1] += m[i]
    if len(set(str(m[-1]))) == 8:
        A235810_list.append(n) # Chai Wah Wu, Nov 05 2014

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

Cf. A000578, A030292, A155146, A018884, A202940.

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 1-8 of 8 results.

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