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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 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 June 20 06:23 EDT 2021. Contains 345157 sequences. (Running on oeis4.)