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

1,2

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.

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

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A239533 A070575 A004505 * A190582 A004457 A248501

Adjacent sequences: A262457 A262458 A262459 * A262461 A262462 A262463

Keyword

nonn,base

Author

Reinhard Zumkeller, Sep 23 2015

Status

approved