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A262460 Lexicographically earliest sequence of distinct terms such that the hexadecimal representations of two consecutive terms overlap.

%I A262460 #13 Feb 16 2025 08:33:27
%S A262460 1,16,17,18,2,32,34,33,19,3,35,48,51,49,20,4,36,50,37,5,21,65,22,6,38,
%T A262460 66,39,7,23,81,24,8,40,82,41,9,25,97,26,10,42,98,43,11,27,113,28,12,
%U A262460 44,114,45,13,29,129,30,14,46,130,47,15,31,145,57,67,52,64
%N A262460 Lexicographically earliest sequence of distinct terms such that the hexadecimal representations of two consecutive terms overlap.
%C A262460 Suggested by Paul Tek's A262323;
%C A262460 two numbers are overlapping if a nonempty prefix of one equals a suffix of the other;
%C A262460 permutation of the natural numbers with inverse A262461.
%H A262460 Reinhard Zumkeller, <a href="/A262460/b262460.txt">Table of n, a(n) for n = 1..10000</a>
%H A262460 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Hexadecimal.html">Hexadecimal</a>
%H A262460 Wikipedia, <a href="http://en.wikipedia.org/wiki/Hexadecimal">Hexadecimal</a>
%H A262460 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A262460 Table of initial terms: the HEX column gives the hexadecimal representation with aligned overlapping digits.
%e A262460 .   n | a(n) | HEX          n | a(n) | HEX          n | a(n) | HEX
%e A262460 . ----+------+-------     ----+------+-------     ----+------+-------
%e A262460 .   1 |    1 |  1          25 |   38 |   26        49 |   44 |    2C
%e A262460 .   2 |   16 |  10         26 |   66 |  42         50 |  114 |   72
%e A262460 .   3 |   17 | 11          27 |   39 |   27        51 |   45 |    2D
%e A262460 .   4 |   18 |  12         28 |    7 |    7        52 |   13 |     D
%e A262460 .   5 |    2 |   2         29 |   23 |   17        53 |   29 |    1D
%e A262460 .   6 |   32 |   20        30 |   81 |  51         54 |  129 |   81
%e A262460 .   7 |   34 |  22         31 |   24 |   18        55 |   30 |    1E
%e A262460 .   8 |   33 |   21        32 |    8 |    8        56 |   14 |     E
%e A262460 .   9 |   19 |    13       33 |   40 |   28        57 |   46 |    2E
%e A262460 .  10 |    3 |     3       34 |   82 |  52         58 |  130 |   82
%e A262460 .  11 |   35 |    23       35 |   41 |   29        59 |   47 |    2F
%e A262460 .  12 |   48 |     30      36 |    9 |    9        60 |   15 |     F
%e A262460 .  13 |   51 |    33       37 |   25 |   19        61 |   31 |    1F
%e A262460 .  14 |   49 |     31      38 |   97 |  61         62 |  145 |   91
%e A262460 .  15 |   20 |      14     39 |   26 |   1A        63 |   57 |  39
%e A262460 .  16 |    4 |       4     40 |   10 |    A        64 |   67 | 43
%e A262460 .  17 |   36 |      24     41 |   42 |   2A        65 |   52 |  34
%e A262460 .  18 |   50 |     32      42 |   98 |  62         66 |   64 |   40
%e A262460 .  19 |   37 |      25     43 |   43 |   2B        67 |   68 |  44
%e A262460 .  20 |    5 |       5     44 |   11 |    B        68 |   69 |   45
%e A262460 .  21 |   21 |      15     45 |   27 |   1B        69 |   80 |    50
%e A262460 .  22 |   65 |     41      46 |  113 |  71         70 |   53 |   35
%e A262460 .  23 |   22 |      16     47 |   28 |   1C        71 |   83 |    53
%e A262460 .  24 |    6 |       6     48 |   12 |    C        72 |   54 |     36
%o A262460 (Haskell)
%o A262460 import Data.List (inits, tails, intersect, delete, genericIndex)
%o A262460 a262460 n = genericIndex a262460_list (n - 1)
%o A262460 a262460_list = 1 : f [1] (drop 2 a262437_tabf) where
%o A262460    f xs tss = g tss where
%o A262460      g (ys:yss) | null (intersect its $ tail $ inits ys) &&
%o A262460                   null (intersect tis $ init $ tails ys) = g yss
%o A262460                 | otherwise = (foldr (\t v -> 16 * v + t) 0 ys) :
%o A262460                               f ys (delete ys tss)
%o A262460      its = init $ tails xs; tis = tail $ inits xs
%Y A262460 Cf. A262323, A262411, A262437, A262461 (inverse).
%K A262460 nonn,base
%O A262460 1,2
%A A262460 _Reinhard Zumkeller_, Sep 23 2015