This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A300653 #7 Mar 11 2018 17:17:45 %S A300653 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, %T A300653 4,16,42,64,128,1,2,4,10,6,32,85,128,256,1,2,4,9,21,9,64,170,256,512, %U A300653 1,2,3,8,18,42,12,128,341,512,1024,1,2,3,4,16,36,85 %N 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). %H A300653 Rémy Sigrist, <a href="/A300653/a300653.gp.txt">PARI program for A300653</a> %F A300653 T(n, 1) = 1. %F A300653 T(n, 2) = 2. %F A300653 T(n, 3) > 3 iff n belongs to A300630. %F A300653 T(2*n, k) = T(n, k). %F A300653 T(1, k) = A000079(k-1). %F A300653 T(3, k) = A000975(k). %F A300653 T(7, k) = A033138(k). %F A300653 T(n, k) = k iff 1 <= k <= A300654(n). %F A300653 T(n, k) = n for some k iff n belongs to A000079 or to A153055. %e A300653 Square array begins: %e A300653 n\k| 1 2 3 4 5 6 7 8 9 10 %e A300653 ---+-------------------------------------------------- %e A300653 1| 1 2 4 8 16 32 64 128 256 512 --> A000079 %e A300653 2| 1 2 4 8 16 32 64 128 256 512 %e A300653 3| 1 2 5 10 21 42 85 170 341 682 --> A000975 %e A300653 4| 1 2 4 8 16 32 64 128 256 512 %e A300653 5| 1 2 3 4 6 9 12 19 25 38 %e A300653 6| 1 2 5 10 21 42 85 170 341 682 %e A300653 7| 1 2 4 9 18 36 73 146 292 585 --> A033138 %e A300653 8| 1 2 4 8 16 32 64 128 256 512 %e A300653 9| 1 2 3 4 6 7 8 12 14 17 %e A300653 10| 1 2 3 4 6 9 12 19 25 38 %o A300653 (PARI) See Links section. %Y A300653 Cf. A000079, A000975, A033138, A153055, A300630, A300654. %K A300653 nonn,base,tabl %O A300653 1,3 %A A300653 _Rémy Sigrist_, Mar 10 2018