A119590 -id:A119590 - cp's OEIS frontend

A119589 Natural numbers from 1 to 100 sorted lexicographically.

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

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

Reinhard Zumkeller, May 06 2011

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

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 (full sequence)

Cf. A190016 (inverse: integers 1..10^4 in lexicographical order).

Cf. A119589, A119590 (integers 1..100 in lexicographical order, and inverse).

import Data.List (elemIndex)
import Data.Maybe (fromJust)
a190017 n = a190017_list !! (n-1)
a190017_list =
   map (succ . fromJust . (`elemIndex` a190016_list)) [1..10000]

A190017=vecsort(A190016=vecsort(vector(10^4,n,Str(n)),,1),,1) \\ 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

A119589 Natural numbers from 1 to 100 sorted lexicographically.

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

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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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