A106001 Start S with 1; extend S with a(n) such that a(n) is the smallest unused integer so far that ends with the a(n)-th digit of S.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 21, 12, 31, 41, 22, 13, 51, 14, 61, 32, 42, 71, 23, 15, 81, 91, 24, 16, 101, 33, 52, 34, 62, 17, 111, 72, 43, 121, 25, 18, 131, 19, 141, 82, 44, 151, 26, 161, 10, 171, 53, 63, 35, 92, 73, 54, 36, 102, 181, 27, 191, 201, 211, 37, 112, 64

Offset: 1

Author

Eric Angelini, Apr 25 2005, revised Dec 06 2007

Keywords

• base
• easy
• nonn
• look

Comments

This is a permutation of the natural numbers as, in building the sequence, we always choose the smallest integer not yet present.

The inverse is A252781. Eric Angelini, Jan 16 2015

Examples

			Last digits are: (1), (2), (3), (4), (5), (6), (7), (8), (9), 1(1), 2(1), 1(2), 3(1), 4(1), 2(2), 1(3), 5(1), 1(4), 6(1), 3(2), 4(2),... which form (1), (2), (3), (4), (5), (6), (7), (8), (9), (1), (1), (2), (1), (1), (2), (3), (1), (4), (1), (2), (2)... then 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 2, 1, 1, 2, 3, 1, 4, 1, 2, 2,... which can be seen as 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 21, 12, 31, 41, 22,... thus the starting sequence.
		

Links

• Paul Tek, Table of n, a(n) for n = 1..10000
• Éric Angelini, The a(n)th term of S ends with the a(n)th digit of S, SeqFan list, Jan 15 2015.
• Paul Tek, PERL program for this sequence
• Index entries for sequences related to final digits of numbers
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A010879, A252781 (inverse), A126968

Programs

Haskell

import Data.List (delete)
a250310 n = a250310_list !! (n-1)
a250310_list = [1..9] ++ [11] ++ f ([0..9] ++ [1,1]) 11 (10 : [12..])
    where f ss i zs = g zs where
        g (x:xs) = if ss !! i /= mod x 10
            then g xs
            else x : f (ss ++ map (read . return) (show x))
                (i + 1) (delete x zs)
-- Reinhard Zumkeller, Jan 16 2015

Extensions

Data corrected by Paul Tek, Aug 11 2013