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.
(See the program at A204979.)
The rectangular array M(n, k) begins: n\k 1 2 3 4 5 6 7 8 9 10 ... 1: 3 7 11 15 19 23 27 31 35 39 2: 7 15 23 31 39 47 55 63 71 79 3: 15 31 47 63 79 95 111 127 143 159 4: 31 63 95 127 159 191 223 255 287 319 5: 63 127 191 255 319 383 447 511 575 639 6: 127 255 383 511 639 767 895 1023 1151 1279 7: 255 511 767 1023 1279 1535 1791 2047 2303 2559 8: 511 1023 1535 2047 2559 3071 3583 4095 4607 5119 9: 1023 2047 3071 4095 5119 6143 7167 8191 9215 10239 10: 2047 4095 6143 8191 10239 12287 14335 16383 18431 20479 ... The triangle TM(m, n) begins (zeros are not shown): m\n 1 2 3 4 5 6 7 8 9 10 ... 1: 3 2: 7 7 3: 11 15 15 4: 15 23 31 31 5: 19 31 47 63 63 6: 23 39 63 95 127 127 7: 27 47 79 127 191 255 255 8: 31 55 95 159 255 383 511 511 9: 35 63 111 191 319 511 767 1023 1023 10: 39 71 127 223 383 639 1023 1535 2047 2047 ... --------------------------------------------------------------------- n=1, ud, k=1: M(1, 1) = 3 = TM(1, 1), N(1,1) = 5 with the Collatz sequence [3, 10, 5] of length 3. n=1, ud, k=2: M(1, 2) = 7 = TM(2, 1), N(1,2) = 11 with the Collatz sequence [7, 22, 11] of length 3. n=4, (ud)^4, k=2: M(4, 2) = 63 = TM(5, 4), N(4,2) = 323 with the Collatz sequence [63, 190, 95, 286, 143, 430, 215, 646, 323] of length 9. n=5, (ud)^5, k=1: M(5, 1) = 63 = TM(5, 5), N(5,1) = 485 with the Collatz sequence [63, 190, 95, 286, 143, 430, 215, 646, 323, 970, 485] of length 11.
1 divides 2^2-2^1, so a(1)=2 2 divides 2^3-2^2, so a(2)=3 3 divides 2^3-2^1, so a(3)=3 4 divides 2^4-2^3, so a(4)=4
s[n_] := s[n] = 2^(n - 1); z1 = 800; z2 = 50;
Table[s[n], {n, 1, 30}] (* A000079 *)
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}] (* A130328 *)
v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
d[n_] := d[n] = First[Delete[w[n], Position[w[n], 0]]]
Table[d[n], {n, 1, z2}] (* A204939 *)
k[n_] := k[n] = Floor[(3 + Sqrt[8 d[n] - 1])/2]
m[n_] := m[n] = Floor[(-1 + Sqrt[8 n - 7])/2]
j[n_] := j[n] = d[n] - m[d[n]] (m[d[n]] + 1)/2
Table[k[n], {n, 1, z2}] (* A204979 *)
Table[j[n], {n, 1, z2}] (* A001511 ? *)
Table[s[k[n]], {n, 1, z2}] (* A204981 *)
Table[s[j[n]], {n, 1, z2}] (* A006519 ? *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A204983 *)
Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A204984 *)
(See the program at A204987.)
First few rows of the triangle:
1;
5, 2;
21, 10, 4;
85, 42, 20, 8;
341, 170, 84, 40, 16;
...
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