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A300653 Square array T(n, k) (n >= 1, k >= 1) read by antidiagonals upwards: T(n, k) is the k-th positive number whose binary representation appears as a substring in the binary representation of 1/n (ignoring the radix point and adding trailing zeros if necessary in case of a terminating expansion). 5
1, 1, 2, 1, 2, 4, 1, 2, 4, 8, 1, 2, 5, 8, 16, 1, 2, 4, 10, 16, 32, 1, 2, 3, 8, 21, 32, 64, 1, 2, 5, 4, 16, 42, 64, 128, 1, 2, 4, 10, 6, 32, 85, 128, 256, 1, 2, 4, 9, 21, 9, 64, 170, 256, 512, 1, 2, 3, 8, 18, 42, 12, 128, 341, 512, 1024, 1, 2, 3, 4, 16, 36, 85 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..73.

Rémy Sigrist, PARI program for A300653

FORMULA

T(n, 1) = 1.

T(n, 2) = 2.

T(n, 3) > 3 iff n belongs to A300630.

T(2*n, k) = T(n, k).

T(1, k) = A000079(k-1).

T(3, k) = A000975(k).

T(7, k) = A033138(k).

T(n, k) = k iff 1 <= k <= A300654(n).

T(n, k) = n for some k iff n belongs to A000079 or to A153055.

EXAMPLE

Square array begins:

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

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

    1|    1    2    4    8   16   32   64  128  256  512  -->  A000079

    2|    1    2    4    8   16   32   64  128  256  512

    3|    1    2    5   10   21   42   85  170  341  682  -->  A000975

    4|    1    2    4    8   16   32   64  128  256  512

    5|    1    2    3    4    6    9   12   19   25   38

    6|    1    2    5   10   21   42   85  170  341  682

    7|    1    2    4    9   18   36   73  146  292  585  -->  A033138

    8|    1    2    4    8   16   32   64  128  256  512

    9|    1    2    3    4    6    7    8   12   14   17

   10|    1    2    3    4    6    9   12   19   25   38

PROG

(PARI) See Links section.

CROSSREFS

Cf. A000079, A000975, A033138, A153055, A300630, A300654.

Sequence in context: A303696 A131074 A059268 * A256009 A123937 A138882

Adjacent sequences:  A300650 A300651 A300652 * A300654 A300655 A300656

KEYWORD

nonn,base,tabl

AUTHOR

Rémy Sigrist, Mar 10 2018

STATUS

approved

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Last modified July 12 04:30 EDT 2020. Contains 335658 sequences. (Running on oeis4.)