Search: id:A140760
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%I A140760
%S A140760 2,6,12,14,24,26,30,28,48,50,54,62,52,58,96,56,60,98,102,110,126,100,
%T A140760 106,118,192,104,108,194,114,122,198,206,222,254,112,124,116,196,202,
%U A140760 214,238,384,120,200,204,386,210,218,390,230,246,398,414,446,510
%N A140760 Irregular table of natural numbers (read by columns) which can be mapped 
               to the source partitions described in A053445 and A126441.
%C A140760 Sequences A000041, A002865 and A053445 count numeric partitions. A125106 
               maps numeric partitions to the natural numbers and has A120 elements 
               per row. A126441 has A41 elements per column and is a tabular arrangement 
               of the natural numbers. A140691 is a rearrangement of table A126441. 
               A140692 extracts the cyclic cases and has A002865 elements per column.
%C A140760 The values for A140760 can also be generated by beginning with A140759 
               and repeatedly multiplying by two as follows:
%C A140760 2
%C A140760 ....6.....12......24.....48.....96
%C A140760 ..........14..........28........56
%C A140760 ..................26........52....
%C A140760 ..................30............60
%C A140760 .........................50.......
%C A140760 .........................54.......
%C A140760 .........................62.......
%C A140760 Note that the number of entries in each column is given by A053445.
%e A140760 The values of A140760 can be obtained by selecting the first even number 
               on each applicable row of Table A126441.
%e A140760 Table A126441 begins
%e A140760 1.2.4..8.16.32.64.128.256.512.1024
%e A140760 .3.5..9.17.33.65.129.257.513.1025
%e A140760 ......6.10.18.34..66.130.258..514
%e A140760 ...7.11.19.35.67.131.259.515.1027
%e A140760 ...........12.20..36..68.132..260
%e A140760 ........13.21.37..69.133.261..517
%e A140760 ...........14.22..38..70.134..262
%e A140760 .....15.23.39.71.135.263.519.1031
%e A140760 ..................24..40..72..136
%e A140760 ..............25..41..73.137..265
%e A140760 ..................26..42..74..138
%e A140760 ...........27.43..75.139.267..523
%e A140760 ......................28..44...76
%e A140760 ..............29..45..77.141..269
%e A140760 ..................30..46..78..142
%e A140760 ........31.47.79.143.271.527.1039
%e A140760 ..........................48...80
%e A140760 ......................49..81..145
%e A140760 ..........................50...82
%e A140760 ..................51..83.147..275
%Y A140760 Cf. A000041, A000120, A002865, A053445, A125106, A126441, A140691, A140692, 
               A140759.
%Y A140760 Sequence in context: A079849 A057895 A111369 this_sequence A161922 A027863 
               A152301
%Y A140760 Adjacent sequences: A140757 A140758 A140759 this_sequence A140761 A140762 
               A140763
%K A140760 nonn,tabf
%O A140760 1,1
%A A140760 Alford Arnold (Alford1940(AT)aol.com), May 28 2008

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