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A322261 Square array T(n, k) (n >= 0, k >= 0) read by antidiagonals upwards: the lengths of runs in binary expansion of T(n, k) correspond to the lengths of runs in binary expansion of n followed by the lengths of runs in binary expansion of k. 0
0, 1, 1, 2, 2, 2, 3, 5, 5, 3, 4, 6, 10, 4, 4, 5, 9, 13, 11, 11, 5, 6, 10, 18, 12, 20, 10, 6, 7, 13, 21, 19, 27, 21, 9, 7, 8, 14, 26, 20, 36, 26, 22, 8, 8, 9, 17, 29, 27, 43, 37, 25, 23, 23, 9, 10, 18, 34, 28, 52, 42, 38, 24, 40, 22, 10, 11, 21, 37, 35, 59, 53 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The array T is associative.

LINKS

Table of n, a(n) for n=0..71.

Index entries for sequences related to binary expansion of n

FORMULA

T(n, 0) = T(0, n) = n.

T(n, 1) = A042963(n+1).

T(n, 2) = A047617(n+1).

T(n, 3) = A047457(n+1).

T(1, n) = A010078(n+1).

T(2, n) = A004757(n) for any n > 0.

A005811(T(n, k)) = A005811(n) + A005811(k).

T(2*n, k) = A163621(2*n, k) for any n > 0 and k > 0.

T(2*n, 2*n) = A020330(2*n) for any n > 0.

EXAMPLE

Array T(n, k) begins (in decimal):

  n\k|  0   1   2   3   4   5   6   7    8    9   10   11   12

  ---+--------------------------------------------------------

    0|  0   1   2   3   4   5   6   7    8    9   10   11   12

    1|  1   2   5   4  11  10   9   8   23   22   21   20   19

    2|  2   5  10  11  20  21  22  23   40   41   42   43   44

    3|  3   6  13  12  27  26  25  24   55   54   53   52   51

    4|  4   9  18  19  36  37  38  39   72   73   74   75   76

    5|  5  10  21  20  43  42  41  40   87   86   85   84   83

    6|  6  13  26  27  52  53  54  55  104  105  106  107  108

    7|  7  14  29  28  59  58  57  56  119  118  117  116  115

    8|  8  17  34  35  68  69  70  71  136  137  138  139  140

Array T(n, k) begins (in binary):

  n\k |     0      1      10      11      100      101      110      111      1000

  ----+---------------------------------------------------------------------------

     0|     0      1      10      11      100      101      110      111      1000

     1|     1     10     101     100     1011     1010     1001     1000     10111

    10|    10    101    1010    1011    10100    10101    10110    10111    101000

    11|    11    110    1101    1100    11011    11010    11001    11000    110111

   100|   100   1001   10010   10011   100100   100101   100110   100111   1001000

   101|   101   1010   10101   10100   101011   101010   101001   101000   1010111

   110|   110   1101   11010   11011   110100   110101   110110   110111   1101000

   111|   111   1110   11101   11100   111011   111010   111001   111000   1110111

  1000|  1000  10001  100010  100011  1000100  1000101  1000110  1000111  10001000

PROG

(PARI) torl(n) = my (r=[]); while (n, r = concat(valuation(n+(n%2), 2), r); n \= 2^r[1]; ); r

fromrl(r) = my (v=0); for (i=1, #r, v = (v + (i%2))*2^r[i]-(i%2)); v

T(n, k) = fromrl(concat(torl(n), torl(k)))

CROSSREFS

Cf. A004757, A005811, A010078, A020330, A042963, A047457, A047617, A101211, A163621.

Sequence in context: A114639 A071867 A126337 * A304718 A036355 A228390

Adjacent sequences:  A322258 A322259 A322260 * A322262 A322263 A322264

KEYWORD

nonn,tabl,base

AUTHOR

Rémy Sigrist, Dec 01 2018

STATUS

approved

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Last modified January 19 03:54 EST 2020. Contains 331031 sequences. (Running on oeis4.)