A106001 - OEIS

%I #24 Apr 21 2023 13:14:20

%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,

%T 24,16,101,33,52,34,62,17,111,72,43,121,25,18,131,19,141,82,44,151,26,

%U 161,10,171,53,63,35,92,73,54,36,102,181,27,191,201,211,37,112,64

%N 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.

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

%C The inverse is A252781. _Eric Angelini_, Jan 16 2015

%H Paul Tek, <a href="/A106001/b106001.txt">Table of n, a(n) for n = 1..10000</a>

%H Éric Angelini, <a href="http://list.seqfan.eu/oldermail/seqfan/2015-January/014300.html">The a(n)th term of S ends with the a(n)th digit of S</a>, SeqFan list, Jan 15 2015.

%H Paul Tek, <a href="/A106001/a106001.txt">PERL program for this sequence</a>

%H <a href="/index/Fi#final">Index entries for sequences related to final digits of numbers</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%e 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.

%o (Haskell)

%o import Data.List (delete)

%o a250310 n = a250310_list !! (n-1)

%o a250310_list = [1..9] ++ [11] ++ f ([0..9] ++ [1,1]) 11 (10 : [12..])

%o     where f ss i zs = g zs where

%o         g (x:xs) = if ss !! i /= mod x 10

%o             then g xs

%o             else x : f (ss ++ map (read . return) (show x))

%o                 (i + 1) (delete x zs)

%o -- Reinhard Zumkeller, Jan 16 2015

%Y Cf. A010879, A252781 (inverse), A126968

%K base,easy,nonn,look

%O 1,2

%A _Eric Angelini_, Apr 25 2005, revised Dec 06 2007

%E Data corrected by _Paul Tek_, Aug 11 2013