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 A201908 Irregular triangle of 2^k mod (2n-1). 10
 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, 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, 11, 3, 6, 12, 5, 10, 1, 2, 4, 8, 16, 11, 1, 2, 4, 8, 16, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 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). 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. REFERENCES Robert L. Devaney, A First Course in Chaotic Dynamical Systems, Addison-Wesley., 1992. pp. 24-25 LINKS T. D. Noe, Rows n = 1..100, flattened FORMULA T(n, k) = 2^k mod (2*n-1), n >= 1, k = 0, 1, ..., A002326(n-1) - 1. 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 EXAMPLE The irregular triangle T(n, k) begins: n\k  0 1 2 3  4  5  6  7 8  9 10 11 12 13 14 15 16 17 ... --------------------------------------------------------- 1:   0 2:   1 2 3:   1 2 4 3 4:   1 2 4 5:   1 2 4 8  7  5 6:   1 2 4 8  5 10  9  7 3  6 7:   1 2 4 8  3  6 12 11 9  5 10  7 8:   1 2 4 8 9:   1 2 4 8 16 15 13  9 10:  1 2 4 8 16 13  7 14 9 18 17 15 11  3  6 12  5 10 ... reformatted by Wolfdieter Lang, Jul 29 2020. MATHEMATICA 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}]] PROG (GAP) R:=List([0..72], n->OrderMod(2, 2*n+1));; 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 CROSSREFS Cf. A002326, A201909 (3^k), A201910 (5^k), A201911 (7^k). 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). Sequence in context: A333442 A319563 A201912 * A337712 A256184 A120855 Adjacent sequences:  A201905 A201906 A201907 * A201909 A201910 A201911 KEYWORD nonn,easy,tabf AUTHOR T. D. Noe, Dec 07 2011 STATUS approved

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Last modified September 21 01:46 EDT 2021. Contains 347596 sequences. (Running on oeis4.)