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 A201908 #28 Oct 06 2020 02:49:53
%S A201908 0,1,2,1,2,4,3,1,2,4,1,2,4,8,7,5,1,2,4,8,5,10,9,7,3,6,1,2,4,8,3,6,12,
%T A201908 11,9,5,10,7,1,2,4,8,1,2,4,8,16,15,13,9,1,2,4,8,16,13,7,14,9,18,17,15,
%U A201908 11,3,6,12,5,10,1,2,4,8,16,11,1,2,4,8,16,9
%N A201908 Irregular triangle of 2^k mod (2n-1).
%C A201908 The length of the rows is given by A002326. For n > 1, the first term of row n is 1 and the last term is n. Many sequences are in this one: starting at A036117 (mod 11) and A070335 (mod 23).
%C A201908 Row n, for n >= 2, divided elementwise by (2*n-1) gives the cycles of iterations of the doubling function D(x) = 2*x or 2*x-1 if 0 <= x < 1/2 or , 1/2 <= x < 1, respectively, with seed 1/(2*n-1). See the Devaney reference, pp. 25-26. D^[k](x) = frac(2^k/(2*n-1)), for k = 0, 1, ..., A002326(n-1) - 1. E.g., n = 3: 1/5, 2/5, 4/5, 3/5. - _Gary W. Adamson_ and _Wolfdieter Lang_, Jul 29 2020.
%D A201908 Robert L. Devaney, A First Course in Chaotic Dynamical Systems, Addison-Wesley., 1992. pp. 24-25
%H A201908 T. D. Noe, <a href="/A201908/b201908.txt">Rows n = 1..100, flattened</a>
%F A201908 T(n, k) = 2^k mod (2*n-1), n >= 1, k = 0, 1, ..., A002326(n-1) - 1.
%F A201908 T(n, k) = (2*n-1)*frac(2^k/(2*n-1)), n >= 1, k = 0, 1, ..., A002326(n-1) - 1, with the fractional part frac(x) = x - floor(x). - _Wolfdieter Lang_, Jul 29 2020
%e A201908 The irregular triangle T(n, k) begins:
%e A201908 n\k 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 ...
%e A201908 ---------------------------------------------------------
%e A201908 1: 0
%e A201908 2: 1 2
%e A201908 3: 1 2 4 3
%e A201908 4: 1 2 4
%e A201908 5: 1 2 4 8 7 5
%e A201908 6: 1 2 4 8 5 10 9 7 3 6
%e A201908 7: 1 2 4 8 3 6 12 11 9 5 10 7
%e A201908 8: 1 2 4 8
%e A201908 9: 1 2 4 8 16 15 13 9
%e A201908 10: 1 2 4 8 16 13 7 14 9 18 17 15 11 3 6 12 5 10
%e A201908 ... reformatted by _Wolfdieter Lang_, Jul 29 2020.
%t A201908 nn = 30; p = 2; t = p^Range[0, nn]; Flatten[Table[If[IntegerQ[Log[p, n]], {0}, tm = Mod[t, n]; len = Position[tm, 1, 1, 2][[-1,1]]; Take[tm, len-1]], {n, 1, nn, 2}]]
%o A201908 (GAP) R:=List([0..72],n->OrderMod(2,2*n+1));;
%o A201908 Flat(Concatenation([0],List([2..11],n->List([0..R[n]-1],k->PowerMod(2,k,2*n-1))))); # _Muniru A Asiru_, Feb 02 2019
%Y A201908 Cf. A002326, A201909 (3^k), A201910 (5^k), A201911 (7^k).
%Y A201908 Cf. A000034 (3), A070402 (5), A069705 (7), A036117 (11), A036118 (13), A062116 (17), A036120 (19), A070347 (21), A070335 (23), A070336 (25), A070337 (27), A036122 (29), A070338 (33), A070339 (35), A036124 (37), A070340 (39), A070348 (41), A070349 (43), A070350 (45), A070351 (47), A036128 (53), A036129 (59), A036130 (61), A036131 (67), A036135 (83), A036138 (101), A036140 (107), A201920 (125), A036144 (131), A036146 (139), A036147 (149), A036150 (163), A036152 (173), A036153 (179), A036154 (181), A036157 (197), A036159 (211), A036161 (227).
%K A201908 nonn,easy,tabf
%O A201908 1,3
%A A201908 _T. D. Noe_, Dec 07 2011