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
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
Programs
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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
Comments