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

1,2

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

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

Example

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.

Prog

(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

Crossrefs

Cf. A010879, A252781 (inverse), A126968

Sequence in context: A275513 A336668 A038724 * A161390 A354081 A096106

Adjacent sequences: A105998 A105999 A106000 * A106002 A106003 A106004

Keyword

base,easy,nonn,look

Author

Eric Angelini, Apr 25 2005, revised Dec 06 2007

Extensions

Data corrected by Paul Tek, Aug 11 2013

Status

approved