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 1-9 of 9 results.

A216192 a(n) = Smallest m >= 5 containing no twos when represented in any base from 3 through n.

Original entry on oeis.org

9, 12, 28, 28, 28, 28, 28, 31
Offset: 3

Views

Author

Nathan Fox, Mar 12 2013

Keywords

Comments

If a(11) exists, it contains over 3000 digits.
No more terms < 10^154400. Most likely there are no more terms. - Chai Wah Wu, Mar 17 2016

Examples

			In base 3, 5=12, 6=20, 7=21, 8=22, 9=100.  The first representation containing no twos is that of 9, so a(3)=9.

Links

Crossrefs

Cf. A216194, A270037, A270038, A270039, A270040, A270041, A270042, A270043, A270044, A270045.

Programs

  • Mathematica
    Table[SelectFirst[Range[5, 10^3], Total@ Map[Function[k, DigitCount[#, k, 2]], Range[3, n]] == 0 &], {n, 3, 20}] /. n_ /; MissingQ@ n -> Nothing (* Michael De Vlieger, Mar 09 2016, Version 10.2 *)

A270037 a(n) = Smallest m >= 3 containing no zeros when represented in any base from 3 through n.

Original entry on oeis.org

4, 5, 7, 7, 13, 13, 13, 13, 13, 13, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157
Offset: 3

Views

Author

Nathan Fox, Mar 09 2016

Keywords

Comments

It remains to be determined if the sequence is finite.
Every known term in this sequence is in A069575, and every term in A069575 is in this sequence.

Links

Crossrefs

Cf. A069575, A270027, A270038, A216192, A270039, A270040, A270041, A270042, A270043, A270044, A270045.

Programs

  • Mathematica
    Table[SelectFirst[Range[3, 10^3], Total@ Map[Function[k, DigitCount[#, k, 0]], Range[3, n]] == 0 &], {n, 3, 80}] /. n_ /; MissingQ@ n -> Nothing (* Michael De Vlieger, Mar 10 2016, Version 10.2 *)
  • PARI
    isok(m, n) = {for (b=3, n, if (! vecmin(digits(m, b)), return (0));); 1;}
a(n) = {my(m = 3); while (! isok(m,n), m++); m;} \\ Michel Marcus, Mar 10 2016

A270034 a(n) is the smallest b for which the base-b representation of n contains at least one 8 (or 0 if no such base exists).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 9, 10, 11, 12, 13, 14, 15, 16, 17, 9, 19, 10, 21, 11, 23, 12, 25, 13, 9, 14, 29, 10, 31, 16, 11, 17, 35, 9, 37, 19, 13, 10, 41, 14, 43, 11, 9, 23, 47, 12, 49, 10, 17, 13, 53, 9, 11, 14, 19, 29, 59, 10, 61, 31, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9
Offset: 1

Views

Author

Nathan Fox, Mar 08 2016

Keywords

Comments

a(n) > 0 for n >= 17 since 18 is n written in base n-8.
The only perfect k-th powers (k >= 2) that can appear in this sequence are m^k with 2 <= m <= 8 and k a prime number.

Links

Crossrefs

Cf. A270027, A270028, A216194, A270029, A270030, A270031, A270032, A270033, A270035, A270044.

Programs

  • Mathematica
    Table[SelectFirst[Range[9, 1200], DigitCount[n, #, 8] > 0 &], {n, 17, 120}] (* Michael De Vlieger, Mar 10 2016, Version 10 *)
  • PARI
    b(n) = if ((n<17) && (n!=8), 0, my(b=9); while(!vecsearch(Set(digits(n, b)), 8), b++); b); \\ Michel Marcus, Mar 10 2016

A270045 Smallest m >= 19 containing no nines when represented in any base from 10 through n.

Original entry on oeis.org

20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 30, 32, 32, 34, 34, 36, 36, 38, 38, 40, 40, 44, 44, 44, 44, 46, 46, 50, 50, 50, 50, 52, 52, 56, 56, 56, 56, 58, 58, 62, 62, 62, 62, 68, 68, 68, 68, 68, 68, 70, 70, 76, 76, 76, 76, 76, 76, 80, 80, 80, 80, 82, 82, 88, 88, 88, 88, 88, 88, 840
Offset: 10

Views

Author

Nathan Fox, Mar 09 2016

Keywords

Comments

It remains to be determined if the sequence is finite.

Links

Crossrefs

Cf. A270035, A270037, A270038, A216192, A270039, A270040, A270041, A270042, A270043, A270044.

Programs

  • Mathematica
    Table[SelectFirst[Range[19, 10^3], Total@ Map[Function[k, DigitCount[#, k, 9]], Range[10, n]] == 0 &], {n, 10, 79}] /. n_ /; MissingQ@ n -> Nothing (* Michael De Vlieger, Mar 10 2016, Version 10.2 *)

A270040 a(n) = Smallest m >= 9 containing no fours when represented in any base from 5 through n.

Original entry on oeis.org

10, 11, 12, 13, 15, 15, 17, 17, 66, 75, 75, 86, 86, 90, 138, 138, 138, 138, 138, 138, 138, 138, 138, 182, 182, 182, 182, 182, 182, 182, 182, 182, 185, 781817578165, 781817578165, 7826560751018861596150680
Offset: 5

Views

Author

Nathan Fox, Mar 09 2016

Keywords

Comments

It remains to be determined if the sequence is finite.
These numbers are not very Foury, at least not initially. (See A268236.)

Links

Crossrefs

Cf. A268236, A268237, A270030, A270037, A270038, A216192, A270039, A270041, A270042, A270043, A270044, A270045.

Programs

  • Mathematica
    Table[SelectFirst[Range[9, 10^3], Total@ Map[Function[k, DigitCount[#, k, 4]], Range[5, n]] == 0 &], {n, 5, 60}] /. n_ /; MissingQ@ n -> Nothing (* Michael De Vlieger, Mar 10 2016, Version 10.2 *)

A270041 a(n) = Smallest m >= 11 containing no fives when represented in any base from 6 through n.

Original entry on oeis.org

12, 13, 14, 15, 16, 18, 18, 20, 20, 22, 22, 24, 24, 28, 28, 28, 28, 144, 144, 160, 160, 162, 216, 216, 216, 216, 216, 216, 216, 216, 216, 223, 228, 316, 316, 316, 316, 316, 316, 316, 316, 316, 316, 316, 316, 316, 316, 487, 487
Offset: 6

Views

Author

Nathan Fox, Mar 09 2016

Keywords

Comments

It remains to be determined if the sequence is finite.

Links

Crossrefs

Cf. A270031, A270037, A270038, A216192, A270039, A270040, A270042, A270043, A270044, A270045.

Programs

  • Mathematica
    Table[SelectFirst[Range[11, 10^3], Total@ Map[Function[k, DigitCount[#, k, 5]], Range[6, n]] == 0 &], {n, 6, 60}] /. n_ /; MissingQ@ n -> Nothing (* Michael De Vlieger, Mar 10 2016, Version 10.2 *)

A270042 a(n) = Smallest m >= 13 containing no sixes when represented in any base from 7 through n.

Original entry on oeis.org

14, 15, 16, 17, 18, 19, 21, 21, 23, 23, 25, 25, 29, 29, 29, 29, 31, 31, 35, 35, 35, 35, 37, 37, 228, 228, 232, 271, 271, 271, 271, 271, 273, 343, 343, 343, 343, 343, 343, 343, 343, 343, 343, 451, 451, 451, 451, 451, 451, 451, 451, 451, 451, 451, 451, 451, 451, 451, 455, 472, 472, 599
Offset: 7

Views

Author

Nathan Fox, Mar 09 2016

Keywords

Comments

It remains to be determined if the sequence is finite.

Links

Crossrefs

Cf. A270032, A270037, A270038, A216192, A270039, A270040, A270041, A270043, A270044, A270045.

Programs

  • Mathematica
    Table[SelectFirst[Range[13, 10^3], Total@ Map[Function[k, DigitCount[#, k, 6]], Range[7, n]] == 0 &], {n, 7, 68}] /. n_ /; MissingQ@ n -> Nothing (* Michael De Vlieger, Mar 10 2016, Version 10.2 *)

A270043 a(n) = Smallest m >= 15 containing no sevens when represented in any base from 8 through n.

Original entry on oeis.org

16, 17, 18, 19, 20, 21, 22, 24, 24, 26, 26, 28, 28, 30, 30, 32, 32, 36, 36, 36, 36, 38, 38, 42, 42, 42, 42, 44, 44, 48, 48, 48, 48, 50, 50, 54, 54, 54, 54, 386, 386, 396, 400, 426, 426, 426, 515, 515, 515, 515, 515, 515, 515, 515, 515, 515, 515, 528
Offset: 8

Views

Author

Nathan Fox, Mar 09 2016

Keywords

Comments

It remains to be determined if the sequence is finite.

Links

Crossrefs

Cf. A270033, A270037, A270038, A216192, A270039, A270040, A270041, A270042, A270044, A270045.

Programs

  • Mathematica
    Table[SelectFirst[Range[15, 10^3], Total@ Map[Function[k, DigitCount[#, k, 7]], Range[8, n]] == 0 &], {n, 8, 65}] /. n_ /; MissingQ@ n -> Nothing (* Michael De Vlieger, Mar 10 2016, Version 10.2 *)

A270038 a(n) = Smallest m >= 3 containing no ones when represented in any base from 3 through n.

Original entry on oeis.org

6, 8, 60, 560, 870899850, 871017138, 871017138, 65473886952, 65473886954
Offset: 3

Views

Author

Nathan Fox, Mar 09 2016

Keywords

Comments

It remains to be determined if the sequence is finite.
a(12) > 3.4*10^30, if it exists. - Giovanni Resta, Oct 14 2019

Crossrefs

Cf. A270028, A270037, A216192, A270039, A270040, A270041, A270042, A270043, A270044, A270045.

Programs

  • Mathematica
    Table[SelectFirst[Range[3, 10^3], Total@ Map[Function[k, DigitCount[#, k, 1]], Range[3, n]] == 0 &], {n, 3, 7}] /. n_ /; MissingQ@ n -> Nothing (* Michael De Vlieger, Mar 10 2016, Version 10.2 *)
Showing 1-9 of 9 results.

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