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

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, 66, 39, 7, 23, 81, 24, 8, 40, 82, 41, 9, 25, 97, 26, 10, 42, 98, 43, 11, 27, 113, 28, 12, 44, 114, 45, 13, 29, 129, 30, 14, 46, 130, 47, 15, 31, 145, 57, 67, 52, 64

Offset: 1

Author

Reinhard Zumkeller, Sep 23 2015

Keywords

• nonn
• base

Comments

Suggested by Paul Tek's A262323;

two numbers are overlapping if a nonempty prefix of one equals a suffix of the other;

permutation of the natural numbers with inverse A262461.

Examples

			Table of initial terms: the HEX column gives the hexadecimal representation with aligned overlapping digits.
.   n | a(n) | HEX          n | a(n) | HEX          n | a(n) | HEX
. ----+------+-------     ----+------+-------     ----+------+-------
.   1 |    1 |  1          25 |   38 |   26        49 |   44 |    2C
.   2 |   16 |  10         26 |   66 |  42         50 |  114 |   72
.   3 |   17 | 11          27 |   39 |   27        51 |   45 |    2D
.   4 |   18 |  12         28 |    7 |    7        52 |   13 |     D
.   5 |    2 |   2         29 |   23 |   17        53 |   29 |    1D
.   6 |   32 |   20        30 |   81 |  51         54 |  129 |   81
.   7 |   34 |  22         31 |   24 |   18        55 |   30 |    1E
.   8 |   33 |   21        32 |    8 |    8        56 |   14 |     E
.   9 |   19 |    13       33 |   40 |   28        57 |   46 |    2E
.  10 |    3 |     3       34 |   82 |  52         58 |  130 |   82
.  11 |   35 |    23       35 |   41 |   29        59 |   47 |    2F
.  12 |   48 |     30      36 |    9 |    9        60 |   15 |     F
.  13 |   51 |    33       37 |   25 |   19        61 |   31 |    1F
.  14 |   49 |     31      38 |   97 |  61         62 |  145 |   91
.  15 |   20 |      14     39 |   26 |   1A        63 |   57 |  39
.  16 |    4 |       4     40 |   10 |    A        64 |   67 | 43
.  17 |   36 |      24     41 |   42 |   2A        65 |   52 |  34
.  18 |   50 |     32      42 |   98 |  62         66 |   64 |   40
.  19 |   37 |      25     43 |   43 |   2B        67 |   68 |  44
.  20 |    5 |       5     44 |   11 |    B        68 |   69 |   45
.  21 |   21 |      15     45 |   27 |   1B        69 |   80 |    50
.  22 |   65 |     41      46 |  113 |  71         70 |   53 |   35
.  23 |   22 |      16     47 |   28 |   1C        71 |   83 |    53
.  24 |    6 |       6     48 |   12 |    C        72 |   54 |     36
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Hexadecimal
• Wikipedia, Hexadecimal
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A262323, A262411, A262437, A262461 (inverse).

Programs

Haskell

import Data.List (inits, tails, intersect, delete, genericIndex)
a262460 n = genericIndex a262460_list (n - 1)
a262460_list = 1 : f [1] (drop 2 a262437_tabf) where
   f xs tss = g tss where
     g (ys:yss) | null (intersect its $ tail $ inits ys) &&
                  null (intersect tis $ init $ tails ys) = g yss
                | otherwise = (foldr (\t v -> 16 * v + t) 0 ys) :
                              f ys (delete ys tss)
     its = init $ tails xs; tis = tail $ inits xs