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

Author

Dmitry Kamenetsky, Jun 01 2006, Jun 03 2006

Keywords

• nonn
• fini
• full
• base

Examples

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

Crossrefs

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

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

Programs

PARI

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

PARI

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

Formula

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