cp's OEIS Frontend

A360470 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, the k rightmost digits of a(n+1) equal the k leftmost digits of a(n) for some k > 0.

%I A360470 #11 Feb 12 2023 10:05:34
%S A360470 1,11,21,2,12,31,3,13,41,4,14,51,5,15,61,6,16,71,7,17,81,8,18,91,9,19,
%T A360470 101,10,110,111,121,112,131,113,141,114,151,115,161,116,171,117,181,
%U A360470 118,191,119,201,20,22,32,23,42,24,52,25,62,26,72,27,82,28,92
%N A360470 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, the k rightmost digits of a(n+1) equal the k leftmost digits of a(n) for some k > 0.
%C A360470 Leading zeros are ignored.
%C A360470 This sequence is a permutation of the positive integers with inverse A360472:
%C A360470 - if a(n) < 10^e, then we can extend the sequence with a number of the form a(n) + k * 10^e (with k > 0),
%C A360470 - by the pigeonhole principle, there are infinitely many terms starting with the same nonzero digit, say with d,
%C A360470 - every number of the form 10*k + d (with k >= 0) appears in the sequence,
%C A360470 - any number v can appear after a term of the form v * 10^k + d (with k > 0).
%H A360470 Rémy Sigrist, <a href="/A360470/b360470.txt">Table of n, a(n) for n = 1..10000</a>
%H A360470 Rémy Sigrist, <a href="/A360470/a360470.png">Scatterplot of the first 1000000 terms</a>
%H A360470 Rémy Sigrist, <a href="/A360470/a360470.gp.txt">PARI program</a>
%H A360470 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A360470 The first terms are:
%e A360470   n   a(n)  a(n) aligned
%e A360470   --  ----  ------------
%e A360470    1     1             1
%e A360470    2    11            11
%e A360470    3    21           21
%e A360470    4     2           2
%e A360470    5    12          12
%e A360470    6    31         31
%e A360470    7     3         3
%e A360470    8    13        13
%e A360470    9    41       41
%e A360470   10     4       4
%e A360470   11    14      14
%e A360470   12    51     51
%o A360470 (PARI) See Links section.
%Y A360470 Cf. A262323, A360472 (inverse).
%K A360470 nonn,base
%O A360470 1,2
%A A360470 _Rémy Sigrist_, Feb 08 2023