A300691 - OEIS

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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, 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 * A377698 A102707 A134486

Adjacent sequences: A300688 A300689 A300690 * A300692 A300693 A300694

KEYWORD

nonn,base,tabl

AUTHOR

Rémy Sigrist, Mar 11 2018

STATUS

approved