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A300691 Square array T(n, k) (n >= 1, k >= 1) read by antidiagonals upwards: T(n, k) is the k-th positive number, say m, such that the binary representation of n appears as a substring in the binary representation of 1/m (ignoring the radix point and adding trailing zeros if necessary in case of a terminating expansion). 1
1, 1, 2, 5, 2, 3, 1, 9, 3, 4, 3, 2, 10, 4, 5, 5, 6, 4, 11, 5, 6, 9, 9, 11, 5, 13, 6, 7, 1, 11, 10, 12, 7, 17, 7, 8, 5, 2, 13, 11, 13, 8, 18, 8, 9, 3, 7, 4, 17, 13, 19, 9, 19, 9, 10, 11, 6, 10, 8, 18, 17, 22, 10, 20, 10, 11, 5, 13, 11, 13, 9, 19, 18, 23, 11, 21 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

If m appears in the n-th row, then 2*m also appears in the n-th row.

This array has connections with A300653: here n appears in 1/T(n, k), there T(n, k) appears in 1/n.

LINKS

Table of n, a(n) for n=1..76.

Rémy Sigrist, PARI program for A300691

FORMULA

T(1, k) = k.

T(2, k) = k.

T(3, k) = A300669(k).

T(n, 1) = A300428(n).

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

T(A000225(i), k) = T(2*A000225(i), k) for any i > 0.

EXAMPLE

Square array begins:

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

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

    1|   1   2   3   4   5   6   7   8   9  10  11  12  -->  A000027

    2|   1   2   3   4   5   6   7   8   9  10  11  12  -->  A000027

    3|   5   9  10  11  13  17  18  19  20  21  22  23  -->  A300669

    4|   1   2   4   5   7   8   9  10  11  13  14  15

    5|   3   6  11  12  13  19  22  23  24  25  26  27

    6|   5   9  10  11  13  17  18  19  20  21  22  23

    7|   9  11  13  17  18  19  22  25  26  27  29  33

    8|   1   2   4   8   9  11  13  15  16  17  18  19

    9|   5   7  10  13  14  19  20  23  26  27  28  29

   10|   3   6  11  12  19  22  24  25  27  29  35  37

   11|  11  13  19  22  23  25  26  27  29  37  38  43

   12|   5   9  10  13  17  18  19  20  21  23  25  26

PROG

(PARI) See Links section.

CROSSREFS

Cf. A000079, A000225, A153055, A300428, A300653, A300669.

Sequence in context: A216022 A100955 A049413 * A102707 A134486 A088006

Adjacent sequences:  A300688 A300689 A300690 * A300692 A300693 A300694

KEYWORD

nonn,base,tabl

AUTHOR

Rémy Sigrist, Mar 11 2018

STATUS

approved

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Last modified September 20 08:13 EDT 2019. Contains 327214 sequences. (Running on oeis4.)