Search: id:A114330
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%I A114330
%S A114330 6,4,38,289,145,203,2603,31826,1157,3827,621101,1388153,2681114,2681669,
%T A114330 121360769,969870257
%N A114330 Smallest semiprime S starting a chain of exactly n semiprimes from iterating 
               f(S) = 2*S+1.
%e A114330 Here are the first 16 terms in order of occurrence with chains through 
               first non-semiprime:
%e A114330 2 4 {4, 9, 19}
%e A114330 1 6 {6, 13}
%e A114330 3 38 {38, 77, 155, 311}
%e A114330 5 145 {145, 291, 583, 1167, 2335, 4671}
%e A114330 6 203 {203, 407, 815, 1631, 3263, 6527, 13055}
%e A114330 4 289 {289, 579, 1159, 2319, 4639}
%e A114330 9 1157 {1157, 2315, 4631, 9263, 18527, 37055, 74111, 148223, 296447, 
               592895}
%e A114330 7 2603 {2603, 5207, 10415, 20831, 41663, 83327, 166655, 333311}
%e A114330 10 3827 {3827, 7655, 15311, 30623, 61247, 122495, 244991, 489983, 979967, 
               1959935, 3919871}
%e A114330 8 31826 {31826, 63653, 127307, 254615, 509231, 1018463, 2036927, 4073855, 
               8147711}
%e A114330 11 621101 {621101, 1242203, 2484407, 4968815, 9937631, 19875263, 39750527, 
               79501055, 159002111, 318004223, 636008447, 1272016895}
%e A114330 12 1388153 {1388153, 2776307, 5552615, 11105231, 22210463, 44420927, 
               88841855, 177683711, 355367423, 710734847, 1421469695, 2842939391, 
               5685878783}
%e A114330 13 2681114 {2681114, 5362229, 10724459, 21448919, 42897839, 85795679, 
               171591359, 343182719, 686365439, 1372730879, 2745461759, 5490923519, 
               10981847039, 21963694079}
%e A114330 14 2681669 {2681669, 5363339, 10726679, 21453359, 42906719, 85813439, 
               171626879, 343253759, 686507519, 1373015039, 2746030079, 5492060159, 
               10984120319, 21968240639, 43936481279}
%e A114330 15 121360769 {121360769, 242721539, 485443079, 970886159, 1941772319, 
               3883544639, 7767089279, 15534178559, 31068357119, 62136714239, 124273428479, 
               248546856959, 497093713919, 994187427839, 1988374855679, 3976749711359}
%e A114330 16 969870257 {969870257, 1939740515, 3879481031, 7758962063, 15517924127, 
               31035848255, 62071696511, 124143393023, 248286786047, 496573572095, 
               993147144191, 1986294288383, 3972588576767, 7945177153535, 15890354307071, 
               31780708614143, 63561417228287}
%e A114330 a(1) = 6 because 6 is semiprime, but 6*2 + 1 = 13 is prime (hence nonsemiprime).
%e A114330 a(2) = 4 because 4 is semiprime, 4*2+1 = 9 (semiprime), but 2*9 + 1 = 
               19 (prime).
%e A114330 a(3) = 38 because 38 is semiprime, 2*38+1 = 77 (semiprime), 2*77+1 = 
               155 (semiprime), but 2*155+1 = 311 (prime).
%Y A114330 Cf. A001358.
%Y A114330 Sequence in context: A163934 A163939 A038258 this_sequence A098657 A112521 
               A109873
%Y A114330 Adjacent sequences: A114327 A114328 A114329 this_sequence A114331 A114332 
               A114333
%K A114330 nonn
%O A114330 0,1
%A A114330 Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 06 2006
%E A114330 Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), who searched 
               through 10^9.

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