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 1-3 of 3 results.

A118761 Fixed points of permutations A118757, A118758, A118759 and A118760.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 119, 138, 157, 176, 195, 310, 339, 358, 377, 396, 559, 578, 597, 779, 798, 999, 3130
Offset: 1

Views

Author

Reinhard Zumkeller, May 01 2006

Keywords

Comments

A118757(a(n)) = A118758(a(n)) = A118759(a(n)) = A118760(a(n)) = a(n);
a(n) = A024657(n-1) = A102491(n) for n<=50.

Crossrefs

Cf. A118767.

A058185 Numbers (written in decimal) which appear the same when written in base 5 and base 10/2.

Original entry on oeis.org

0, 1, 2, 3, 4, 10, 11, 12, 13, 14, 20, 21, 22, 23, 24, 50, 51, 52, 53, 54, 60, 61, 62, 63, 64, 70, 71, 72, 73, 74, 100, 101, 102, 103, 104, 110, 111, 112, 113, 114, 120, 121, 122, 123, 124, 250, 251, 252, 253, 254, 260, 261, 262, 263, 264, 270, 271, 272, 273, 274
Offset: 1

Views

Author

Henry Bottomley, Nov 17 2000

Keywords

Comments

To represent a number in base b, if a digit exceeds b-1, subtract b and carry 1. In fractional base b/c, subtract b and carry c. The sequence consists of numbers which in base 5 only have even digits, or one more than such numbers.

Examples

			10 is a term since it is written as 20 both in base 5 and base 10/2.
40 it not a term since it is written as 130 in base 5 and 80 in base 10/2.

Links

Crossrefs

Cf. A007091, A024657, A058186.

Programs

  • Mathematica
    s[n_] := s[n] = If[n == 0, 0, 10 * s[2 * Floor[n/10]] + Mod[n, 10]]; q[k_] := s[k] == FromDigits[IntegerDigits[k, 5]]; Select[Range[0, 300], q] (* Amiram Eldar, Aug 02 2025 *)
  • PARI
    s(n) = if(n == 0, 0, 10 * s(n\10 * 2) + n % 10);
isok(k) = s(k) == fromdigits(digits(k, 5)); \\ Amiram Eldar, Aug 02 2025

Extensions

Offset corrected by Amiram Eldar, Aug 02 2025

A058186 Numbers (written in base 5) which appear the same when written in base 5 and base 10/2.

Original entry on oeis.org

0, 1, 2, 3, 4, 20, 21, 22, 23, 24, 40, 41, 42, 43, 44, 200, 201, 202, 203, 204, 220, 221, 222, 223, 224, 240, 241, 242, 243, 244, 400, 401, 402, 403, 404, 420, 421, 422, 423, 424, 440, 441, 442, 443, 444, 2000, 2001, 2002, 2003, 2004, 2020, 2021, 2022, 2023
Offset: 1

Views

Author

Henry Bottomley, Nov 17 2000

Keywords

Comments

To represent a number in base b, if a digit exceeds b-1, subtract b and carry 1. In fractional base b/c, subtract b and carry c. The sequence consists of numbers which in base 5 have digits in {0,2,4} except that the unit digit can be any from {0,1,2,3,4}.

Examples

			20 (10 in decimal) is a term since it is written as 20 both in base 5 and base 10/2.
30 (15 in decimal) is not a term since it is written as 30 in base 5 and 25 in base 10/2.

Links

Crossrefs

Cf. A007091, A024657, A058185.

Programs

  • Mathematica
    s[n_] := s[n] = If[n == 0, 0, 10*s[2*Floor[n/10]] + Mod[n, 10]]; f[n_] := FromDigits[IntegerDigits[n, 5]]; q[k_] := s[k] == f[k]; f /@ Select[Range[0, 300], q] (* Amiram Eldar, Aug 02 2025 *)
  • PARI
    s(n) = if(n == 0, 0, 10 * s(n\10 * 2) + n % 10);
f(n) = fromdigits(digits(n, 5));
list(lim) = apply(f, select(x -> s(x) == f(x), vector(lim+1, i, i-1))); \\ Amiram Eldar, Aug 02 2025

Formula

a(n) = A007091(A058185(n)). - Amiram Eldar, Aug 02 2025

Extensions

Offset corrected by Amiram Eldar, Aug 02 2025
Showing 1-3 of 3 results.

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

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