

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.


2



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
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OFFSET

1,2


COMMENTS

This is a permutation of the natural numbers as, in building the sequence, we always chose the smallest integer not yet present in it.
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 !! (n1)
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: A267771 A275513 A038724 * A161390 A096106 A076641
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



