A114330 - OEIS

%I #5 Mar 30 2012 18:40:35

%S 6,4,38,289,145,203,2603,31826,1157,3827,621101,1388153,2681114,

%T 2681669,121360769,969870257

%N Smallest semiprime S starting a chain of exactly n semiprimes from iterating f(S) = 2*S+1.

%e Here are the first 16 terms in order of occurrence with chains through first non-semiprime:

%e 2 4 {4, 9, 19}

%e 1 6 {6, 13}

%e 3 38 {38, 77, 155, 311}

%e 5 145 {145, 291, 583, 1167, 2335, 4671}

%e 6 203 {203, 407, 815, 1631, 3263, 6527, 13055}

%e 4 289 {289, 579, 1159, 2319, 4639}

%e 9 1157 {1157, 2315, 4631, 9263, 18527, 37055, 74111, 148223, 296447, 592895}

%e 7 2603 {2603, 5207, 10415, 20831, 41663, 83327, 166655, 333311}

%e 10 3827 {3827, 7655, 15311, 30623, 61247, 122495, 244991, 489983, 979967, 1959935, 3919871}

%e 8 31826 {31826, 63653, 127307, 254615, 509231, 1018463, 2036927, 4073855, 8147711}

%e 11 621101 {621101, 1242203, 2484407, 4968815, 9937631, 19875263, 39750527, 79501055, 159002111, 318004223, 636008447, 1272016895}

%e 12 1388153 {1388153, 2776307, 5552615, 11105231, 22210463, 44420927, 88841855, 177683711, 355367423, 710734847, 1421469695, 2842939391, 5685878783}

%e 13 2681114 {2681114, 5362229, 10724459, 21448919, 42897839, 85795679, 171591359, 343182719, 686365439, 1372730879, 2745461759, 5490923519, 10981847039, 21963694079}

%e 14 2681669 {2681669, 5363339, 10726679, 21453359, 42906719, 85813439, 171626879, 343253759, 686507519, 1373015039, 2746030079, 5492060159, 10984120319, 21968240639, 43936481279}

%e 15 121360769 {121360769, 242721539, 485443079, 970886159, 1941772319, 3883544639, 7767089279, 15534178559, 31068357119, 62136714239, 124273428479, 248546856959, 497093713919, 994187427839, 1988374855679, 3976749711359}

%e 16 969870257 {969870257, 1939740515, 3879481031, 7758962063, 15517924127, 31035848255, 62071696511, 124143393023, 248286786047, 496573572095, 993147144191, 1986294288383, 3972588576767, 7945177153535, 15890354307071, 31780708614143, 63561417228287}

%e a(1) = 6 because 6 is semiprime, but 6*2 + 1 = 13 is prime (hence nonsemiprime).

%e a(2) = 4 because 4 is semiprime, 4*2+1 = 9 (semiprime), but 2*9 + 1 = 19 (prime).

%e a(3) = 38 because 38 is semiprime, 2*38+1 = 77 (semiprime), 2*77+1 = 155 (semiprime), but 2*155+1 = 311 (prime).

%Y Cf. A001358.

%K nonn

%O 0,1

%A _Jonathan Vos Post_, Feb 06 2006

%E Extended by _Ray Chandler_, who searched through 10^9.