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 1-10 of 13 results. Next

A266549 Number of 2n-step 2-dimensional closed self-avoiding paths on square lattice, reduced for symmetry, i.e., where rotations and reflections are not counted as distinct.

Original entry on oeis.org

0, 1, 1, 3, 6, 25, 86, 414, 1975, 10479, 56572, 316577, 1800363, 10419605, 61061169, 361978851
Offset: 1

Views

Author

Luca Petrone, Dec 31 2015

Keywords

Comments

Differs from A057730 beginning at n = 8, since that sequence includes polyominoes with holes.

Links

Crossrefs

Apparently lim A002931(n)/a(n) = 8 for increasing n, accounting for (in most cases) 4 rotations times two flips. - Joerg Arndt, Hugo Pfoertner, Jul 09 2018
Cf. A010566, A037245 (open self-avoiding walks), A316194.

Extensions

a(11)-a(16) from Joerg Arndt, Jan 25 2018

A270027 a(n) is the smallest b >= 3 for which the base-b representation of n contains at least one 0 (or 0 if no such base exists).

Original entry on oeis.org

0, 0, 3, 4, 5, 3, 7, 4, 3, 3, 3, 3, 13, 7, 3, 4, 4, 3, 3, 3, 3, 11, 23, 3, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 6, 3, 43, 4, 3, 3, 3, 3, 4, 4, 3, 4, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 4, 4, 3, 3, 3, 3, 4, 4, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3
Offset: 1

Views

Author

Nathan Fox, Mar 08 2016

Keywords

Comments

It is natural to consider this sequence starting from base 3 instead of base 2, as the latter causes most terms to be 2 (see A270026).
a(n) = n if and only if n = 3 or n is in A069575.
a(n) > 0 for n >= 3 since the base-n representation of n is 10.

Links

Crossrefs

Cf. A069575, A270026, A270028, A216194, A270029, A270030, A270031, A270033, A270034, A270035, A270037.

Programs

  • Mathematica
    Table[SelectFirst[Range[3, 10^3], DigitCount[n, #, 0] > 0 &], {n, 3, 120}] (* Michael De Vlieger, Mar 10 2016, Version 10 *)
  • PARI
    a(n) = if (n < 3, 0, my(b=3); while(vecmin(digits(n, b)), b++); b); \\ Michel Marcus, Mar 10 2016

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 *)

A270028 a(n) is the smallest b >= 3 for which the base-b representation of n contains at least one 1 (or 0 if no such base exists).

Original entry on oeis.org

3, 0, 3, 3, 3, 4, 3, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 5, 3, 3, 3, 6, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3
Offset: 1

Views

Author

Nathan Fox, Mar 08 2016

Keywords

Comments

If we drop the b >= 3 requirement, then this sequence becomes A007395 (the constant 2 sequence).
a(n) > 0 for n >= 3 since the base-(n-1) representation of n is 11.
a(n)=3 if and only if n is in A081606.
The only perfect k-th powers (k >= 2) that can appear in this sequence are 2^k with k a prime number.
The first n for which a(n)=7 is 560.
The first n for which a(n)=8 is 870899850.
The first n for which a(n)=10 is 871017138.
The first n for which a(n)=11 is 65473886952.
The first n for which a(n)=12 is 65473886954.

Links

Crossrefs

Cf. A270027, A216194, A270029, A270030, A270031, A270033, A270034, A270035, A270038.

Programs

  • Mathematica
    Table[SelectFirst[Range[3, 10], DigitCount[n, #, 1] > 0 &], {n, 3, 120}] (* Michael De Vlieger, Mar 10 2016, Version 10 *)
  • PARI
    a(n) = if (n==2, 0, my(b=3); while(!vecsearch(Set(digits(n, b)), 1), b++); b); \\ Michel Marcus, Mar 10 2016

A270029 a(n) is the smallest b for which the base-b representation of n contains at least one 3 (or 0 if no such base exists).

Original entry on oeis.org

0, 0, 4, 0, 0, 0, 4, 5, 6, 7, 4, 4, 4, 4, 4, 5, 5, 5, 4, 6, 6, 6, 4, 7, 7, 7, 4, 4, 4, 4, 4, 9, 5, 9, 4, 10, 10, 5, 4, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 17, 5, 5, 4, 5, 5, 7, 4, 7, 5, 7, 4, 4, 4, 4, 4, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 5, 4, 4, 4, 4, 4, 5, 5, 5, 4, 26
Offset: 1

Views

Author

Nathan Fox, Mar 08 2016

Keywords

Comments

a(n) > 0 for n >= 7 since 13 is n written in base n-3.
The only perfect k-th powers (k >= 2) that can appear in this sequence are 2^k and 3^k with k a prime number.

Links

Crossrefs

Cf. A270027, A270028, A216194, A270030, A270031, A270032, A270033, A270034, A270035, A270039.

Programs

  • Mathematica
    Table[SelectFirst[Range[4, 10^3], DigitCount[n, #, 3] > 0 &], {n, 7, 120}] (* Michael De Vlieger, Mar 10 2016, Version 10 *)
  • PARI
    a(n) = if ((n<7) && (n!=3), 0, my(b=4); while(!vecsearch(Set(digits(n, b)), 3), b++); b); \\ Michel Marcus, Mar 10 2016

A270030 a(n) is the smallest b for which the base-b representation of n contains at least one 4 (or 0 if no such base exists).

Original entry on oeis.org

0, 0, 0, 5, 0, 0, 0, 0, 5, 6, 7, 8, 9, 5, 11, 6, 13, 7, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 5, 7, 7, 7, 7, 5, 8, 8, 8, 8, 5, 6, 9, 9, 9, 5, 5, 5, 5, 5, 5, 11, 11, 6, 7, 5, 12, 12, 12, 6, 5, 6, 6, 6, 6, 5, 6, 14, 7, 8, 5, 5, 5, 5, 5, 5, 16, 6, 7, 7, 5, 7, 7, 6, 7, 5, 9, 18, 18, 6, 5, 19
Offset: 1

Views

Author

Nathan Fox, Mar 08 2016

Keywords

Comments

a(n) > 0 for n >= 9 since 14 is n written in base n-4.
The only perfect k-th powers (k >= 2) that can appear in this sequence are 2^k, 3^k, or 4^k, with k a prime number.

Links

Crossrefs

Cf. A268236, A268237, A270027, A270028, A216194, A270029, A270031, A270032, A270033, A270034, A270035, A270040.

Programs

  • Mathematica
    Table[SelectFirst[Range[5, 10^3], DigitCount[n, #, 4] > 0 &], {n, 9, 120}] (* Michael De Vlieger, Mar 10 2016, Version 10 *)
  • PARI
    a(n) = if ((n<9) && (n!=4), 0, my(b=5); while(!vecsearch(Set(digits(n, b)), 4), b++); b); \\ Michel Marcus, Mar 10 2016

A270031 a(n) is the smallest b for which the base-b representation of n contains at least one 5 (or 0 if no such base exists).

Original entry on oeis.org

0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 6, 7, 8, 9, 10, 11, 6, 13, 7, 15, 8, 17, 6, 19, 10, 7, 11, 23, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 6, 8, 8, 8, 8, 8, 6, 9, 9, 9, 9, 9, 6, 7, 10, 10, 10, 10, 6, 11, 7, 11, 11, 11, 6, 6, 6, 6, 6, 6, 6, 13, 13, 13, 7, 13, 6, 14, 14, 14, 14, 7, 6, 7, 7, 7, 7, 7
Offset: 1

Views

Author

Nathan Fox, Mar 08 2016

Keywords

Comments

a(n) > 0 for n >= 11 since 15 is n written in base n-5.
The only perfect k-th powers (k >= 2) that can appear in this sequence are m^k with 2 <= m <= 5 and k a prime number.

Links

Crossrefs

Cf. A270027, A270028, A216194, A270029, A270030, A270032, A270033, A270034, A270035, A270041.

Programs

  • Mathematica
    Table[SelectFirst[Range[6, 10^3], DigitCount[n, #, 5] > 0 &], {n, 11, 120}] (* Michael De Vlieger, Mar 10 2016, Version 10 *)
  • PARI
    a(n) = if ((n<11) && (n!=5), 0, my(b=6); while(!vecsearch(Set(digits(n, b)), 5), b++); b); \\ Michel Marcus, Mar 10 2016

A270033 a(n) is the smallest b for which the base-b representation of n contains at least one 7 (or 0 if no such base exists).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 9, 10, 11, 12, 13, 14, 15, 8, 17, 9, 19, 10, 21, 11, 23, 8, 25, 13, 9, 14, 29, 10, 31, 8, 11, 17, 35, 9, 37, 19, 13, 8, 41, 14, 43, 11, 9, 23, 47, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 8, 10, 10, 10, 10, 10, 10, 10, 8, 11, 11
Offset: 1

Views

Author

Nathan Fox, Mar 08 2016

Keywords

Comments

a(n) > 0 for n >= 15 since 17 is n written in base n-7.
The only perfect k-th powers (k >= 2) that can appear in this sequence are m^k with 2 <= m <= 7 and k a prime number.

Links

Crossrefs

Cf. A270027, A270028, A216194, A270029, A270030, A270031, A270032, A270034, A270035, A270043.

Programs

  • Mathematica
    Table[SelectFirst[Range[8, 1200], DigitCount[n, #, 7] > 0 &], {n, 15, 120}] (* Michael De Vlieger, Mar 10 2016, Version 10 *)
  • PARI
    a(n) = if ((n<15) && (n!=7), 0, my(b=8); while(!vecsearch(Set(digits(n, b)), 7), b++); b); \\ 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

A270035 a(n) is the smallest b for which the base-b representation of n contains at least one 9 (or 0 if no such base exists).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 10, 21, 11, 23, 12, 25, 13, 27, 14, 29, 10, 31, 16, 11, 17, 35, 12, 37, 19, 13, 10, 41, 14, 43, 11, 15, 23, 47, 12, 49, 10, 17, 13, 53, 18, 11, 14, 19, 29, 59, 10, 61, 31, 21, 16, 13, 11, 67, 17, 23, 10, 71
Offset: 1

Views

Author

Nathan Fox, Mar 08 2016

Keywords

Comments

a(n) > 0 for n >= 19 since 19 is n written in base n-9.
The only perfect k-th powers (k >= 2) that can appear in this sequence are m^k with 2 <= m <= 9 and k a prime number.

Links

Crossrefs

Cf. A270027, A270028, A216194, A270029, A270030, A270031, A270032, A270033, A270034, A270045.

Programs

  • Mathematica
    Table[SelectFirst[Range[10, 1200], DigitCount[n, #, 9] > 0 &], {n, 19, 120}] (* Michael De Vlieger, Mar 10 2016, Version 10 *)
  • PARI
    a(n) = if ((n<19) && (n!=9), 0, my(b=10); while(!vecsearch(Set(digits(n, b)), 9), b++); b); \\ Michel Marcus, Mar 10 2016
Showing 1-10 of 13 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.