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%I #8 Mar 11 2018 17:17:15
%S 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,
%T 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,
%U 18,17,22,10,20,10,11,5,13,11,13,9,19,18,23,11,21
%N 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).
%C If m appears in the n-th row, then 2*m also appears in the n-th row.
%C This array has connections with A300653: here n appears in 1/T(n, k), there T(n, k) appears in 1/n.
%H Rémy Sigrist, <a href="/A300691/a300691.gp.txt">PARI program for A300691</a>
%F T(1, k) = k.
%F T(2, k) = k.
%F T(3, k) = A300669(k).
%F T(n, 1) = A300428(n).
%F T(n, k) = n for some k iff n belongs to A000079 or to A153055.
%F T(A000225(i), k) = T(2*A000225(i), k) for any i > 0.
%e Square array begins:
%e n\k| 1 2 3 4 5 6 7 8 9 10 11 12
%e ---+------------------------------------------------
%e 1| 1 2 3 4 5 6 7 8 9 10 11 12 --> A000027
%e 2| 1 2 3 4 5 6 7 8 9 10 11 12 --> A000027
%e 3| 5 9 10 11 13 17 18 19 20 21 22 23 --> A300669
%e 4| 1 2 4 5 7 8 9 10 11 13 14 15
%e 5| 3 6 11 12 13 19 22 23 24 25 26 27
%e 6| 5 9 10 11 13 17 18 19 20 21 22 23
%e 7| 9 11 13 17 18 19 22 25 26 27 29 33
%e 8| 1 2 4 8 9 11 13 15 16 17 18 19
%e 9| 5 7 10 13 14 19 20 23 26 27 28 29
%e 10| 3 6 11 12 19 22 24 25 27 29 35 37
%e 11| 11 13 19 22 23 25 26 27 29 37 38 43
%e 12| 5 9 10 13 17 18 19 20 21 23 25 26
%o (PARI) See Links section.
%Y Cf. A000079, A000225, A153055, A300428, A300653, A300669.
%K nonn,base,tabl
%O 1,3
%A _Rémy Sigrist_, Mar 11 2018