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.

A119590 a(n) = position of n in the lexicographical ordering A119589 of natural numbers from 1 to 100.

Original entry on oeis.org

1, 13, 24, 35, 46, 57, 68, 79, 90, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3
Offset: 1

Views

Author

Dmitry Kamenetsky, Jun 01 2006, Jun 03 2006

Keywords

Comments

Inverse of the permutation A119589. - M. F. Hasler, Oct 26 2019

Examples

			a(1) = 1
a(10) = 2 because "10" comes after "1"
a(100) = 3 because "100" comes after "10", but before "11"

Crossrefs

Cf. A119589 (integers 1..100 in lexicographical order).
Cf. A190016, A190017 (integers 1..10^4 in lexicographical order, and inverse).

Programs

  • PARI
    vecsort(vecsort(vector(100,n,Str(n)),,1),,1) \\ M. F. Hasler, Sep 03 2018, simplified Oct 25 2019

Formula

a(n) = a(n-1) + a(n-10) - a(n-11) for 21 < n < 100. - M. F. Hasler, Sep 03 2018
a(n) = k such that A119589(k) = n. - M. F. Hasler, Oct 26 2019

A190016 Numbers 1 through 10000 sorted lexicographically in decimal representation.

Original entry on oeis.org

1, 10, 100, 1000, 10000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 101, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 102, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 103, 1030, 1031, 1032, 1033, 1034, 1035, 1036
Offset: 1

Views

Author

Reinhard Zumkeller, May 06 2011

Keywords

Comments

A190017 = inverse permutation: a(A190017(n)) = A190017(a(n)) = n;
there are 11 fixed points: {1,9980,9981,9982,9983,9984,9985,9986,9987,9988,9989}.

Examples

			a(13) = 1008;
a(14) = 1009;
a(15) = 101;
a(16) = 1010;
a(17) = 1011;
largest term a(5) = 10000;
last term a(10000) = 9999, largest term lexicographically.

Links

Crossrefs

Cf. A119589 (same for 1..100); A190126 (base 2), A190128 (base 3), A190130 (base 8), A190132 (base 12), A190134 (base 16).

Programs

  • Haskell
    import Data.Ord (comparing)
import Data.List (sortBy)
a190016 n = a190016_list !! (n-1)
a190016_list = sortBy (comparing show) [1..10000]
  • PARI
    eval(Set(vector(10^4,n,Str(n)))) \\ M. F. Hasler, Oct 25 2019

A190017 Inverse permutation to A190016: lexicographical ordering of integers 1 .. 10^4.

Original entry on oeis.org

1, 1113, 2224, 3335, 4446, 5557, 6668, 7779, 8890, 2, 114, 225, 336, 447, 558, 669, 780, 891, 1002, 1114, 1225, 1336, 1447, 1558, 1669, 1780, 1891, 2002, 2113, 2225, 2336, 2447, 2558, 2669, 2780, 2891, 3002, 3113, 3224, 3336, 3447, 3558, 3669, 3780, 3891
Offset: 1

Views

Author

Reinhard Zumkeller, May 06 2011

Keywords

Comments

a(A190016(n)) = A190016(a(n)) = n.

Links

Crossrefs

Cf. A190016 (inverse: integers 1..10^4 in lexicographical order).
Cf. A119589, A119590 (integers 1..100 in lexicographical order, and inverse).

Programs

  • Haskell
    import Data.List (elemIndex)
import Data.Maybe (fromJust)
a190017 n = a190017_list !! (n-1)
a190017_list =
   map (succ . fromJust . (`elemIndex` a190016_list)) [1..10000]
  • PARI
    A190017=vecsort(A190016=vecsort(vector(10^4,n,Str(n)),,1),,1) \\ M. F. Hasler, Oct 26 2019

A309589 Number subsets {0, ..., 10^k - 1} written in base 10 and sorted lexicographically, for k = 1, 2, ...

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 2, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 3, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 4, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 5, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 6, 60, 61
Offset: 0

Views

Author

Georg Fischer, Mar 02 2019

Keywords

Comments

The sequence is the flattened form of an irregular table T(k, i). The rows for k >= 1 contain a permutation of the numbers 0 <= i <= 10^k - 1 which is defined by the lexicographical order of the numbers i written in base 10.
This "useless" order appears, for example, in a directory listing of numbered filenames, or after an ASCII sort of signatures of linear recurrences. The Perl program in the link computes this sequence and variations with different ranges and bases.

Examples

			Table T(k, i) begins:
  k\i   0   1   2   3 ...
  -------------------------
  1:    0   1   2   3 ...   9
  2:    0   1  10  11 ...  19   2  20  21 ...  99
  3:    0   1  10 100 ... 109  11 110 111 ... 999
  4:  ...

Links

  • Georg Fischer, Perl program which generates this sequence and its inverse.

Crossrefs

Cf. A119589 (like row k=2, but 1 <= i <= 100), A190016 (like row k=4, but 1 <= i <= 10000), A309590 (inverse)

Programs

  • Perl
    # cf. link
Showing 1-4 of 4 results.

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

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