A300691 - cp's OEIS frontend

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).

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

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