A190017 -id:A190017 - cp's OEIS frontend

A190016 Numbers 1 through 10000 sorted lexicographically in decimal representation.

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

Reinhard Zumkeller, May 06 2011

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}.

			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.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 (full sequence)
Eric Weisstein, Lexicographic Order.
Wikipedia, Lexicographical order.

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

import Data.Ord (comparing)
import Data.List (sortBy)
a190016 n = a190016_list !! (n-1)
a190016_list = sortBy (comparing show) [1..10000]

eval(Set(vector(10^4,n,Str(n)))) \\ M. F. Hasler, Oct 25 2019

A119589 Natural numbers from 1 to 100 sorted lexicographically.

Original entry on oeis.org

1, 10, 100, 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, 62, 63, 64, 65, 66, 67, 68, 69, 7, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 8, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 9, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99

Offset: 1

Dmitry Kamenetsky, Jun 01 2006, Jun 03 2006

			a(1) = 1.
a(2) = 10 because "10" > "1".
a(3) = 100 because "100" > "10", but "100" < "11".

Cf. A119590 (inverse permutation: position of n in this sequence).

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

A119589=vecsort(vector(100,n,Str(n)),,1) \\ M. F. Hasler, Sep 03 2018, edited Oct 25 2019

a(n)=if(n<4, 10^n\10, n=divrem(n+8, 11); n[2]<10, [10,1]*n, n[1]+1) \\ M. F. Hasler, Oct 26 2019

a(n) = if n < 4 then 10^(n-1) else if r < 10 then 10*q + r else q + 1, where [q,r] are the base-11 digits of n+8. - M. F. Hasler, Oct 26 2019

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

Dmitry Kamenetsky, Jun 01 2006, Jun 03 2006

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

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

Cf. A119589 (integers 1..100 in lexicographical order).

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

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

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

A309590 Inverse of A309589: 0-based positions in the 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, 12, 23, 34, 45, 56, 67, 78, 89, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55

Offset: 0

Georg Fischer, Mar 02 2019

The sequence is related to the flattened form of the irregular table T(k, i) described in A309589. There, 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.

The sequence here lists, per sorted row k, the 0-based positions of the numbers i in that row. The positions in row k are also a permutation of the numbers 0 <= i <= 10^k - 1.

Georg Fischer, Perl program which generates A309589 and this sequence.

Cf. A119590 (like row k=2, but i = 1..100), A190017 (like row k=4, but for i = 1..10000), A309589.

Perl
```
# cf. link
```

cp's OEIS Frontend

A190016 Numbers 1 through 10000 sorted lexicographically in decimal representation.

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A119589 Natural numbers from 1 to 100 sorted lexicographically.

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PARI

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

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PARI

Formula

A309590 Inverse of A309589: 0-based positions in the number subsets {0, ..., 10^k - 1} written in base 10 and sorted lexicographically, for k = 1, 2, ...

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Perl