[seqfan] Exchange rightmost two base-4 digits of n>1; a(0)=0, a(1)=4. (base 4 analogue of what A181099 is in base 3, and A080412 is base 2
Jonathan Post
jvospost3 at gmail.com
Mon Oct 11 09:02:31 CEST 2010
Is this right? Would anyone like to code the general base k analogue for k>4?
The scatterplot from graphing A181099 is a chain of 3x3 lozenges of 9
datapoints each, showing the mod 9 pattern of the sequence; just as
scatterplot from graphing A080412 is a chain of 2x2 lozenges of 4
datapoints each, showing the mod 4 pattern of the sequence.
Hence the scatterplot from graphing the new seq is a chain of 4x4
lozenges of 16 datapoints each, showing the mod 16 pattern of the
sequence.
Exchange rightmost two base-4 digits of n>1; a(0)=0, a(1)=4.
0, 4, 8, 12, 1, 5, 9, 13, 2, 6, 10, 14, 3, 7, 11, 15, 16, 20, 24, 28,
17, 21, 25, 29, 18, 22, 26, 30, 19, 23, 27, 31, 32, 36, 40, 44, 33,
37, 41, 45, 34, 38, 42, 46, 35, 39, 43, 47, 48, 52, 56, 60, 49, 53,
57, 61, 50
This is to A007090 Numbers in base 4 as A181099 is to A007089 Numbers
in base 3, and as A080412 is to A007088 Numbers written in base 2.
a(a(n)) = n.
Offset 0,2
n a(n)
a(0) 0 by definition
a(1) 4 by definition
a(2) a(‘02’) = 20 = 8
a(3) a(‘03’) = 30 = 12
a(4) a(‘10’) = 01 = 1
a(5) a(‘11’) = 11 = 5
a(6) a(‘12’) = 21 = 9
a(7) a(‘13’) = 31 = 13
a(8) a(‘20’) = 02 = 2
a(9) a(‘21’) = 12 = 6
a(10) a(‘22’) = 22 = 10
a(11) a(‘23’) = 32 = 14
a(12) a(‘30’) = 03 = 3
a(13) a(‘31’) = 13 = 7
a(14) a(‘32’) = 23 = 11
a(15) a(‘33’) = 33 = 15
a(16) a(‘100’) = 100 = 16
a(17) a(‘101’) = 110 = 20
a(18) a(‘102’) = 120 = 24
a(19) a(‘103’) = 130 = 28
a(20) a(‘110’) = 101 = 17
a(21) a(‘111’) = 111 = 21
a(22) a(‘112’) = 121 = 25
a(23) a(‘113’) = 131 = 29
a(24) a(‘120’) = 102 = 18
a(25) a(‘121’) = 112 = 22
a(26) a(‘122’) = 122 = 26
a(27) a(‘123’) = 132 = 30
a(28) a(‘130’) = 103 = 19
a(29) a(‘131’) = 113 = 23
a(30) a(‘132’) = 123 = 27
a(31) a(‘133’) = 133 = 31
a(32) a(‘200’) = 200 = 32
a(33) a(‘201’) = 210 = 36
a(34) a(‘202’) = 220 = 40
a(35) a(‘203’) = 230 = 44
a(36) a(‘210’) = 201 = 33
a(37) a(‘211’) = 211 = 37
a(38) a(‘212’) = 221 = 41
a(39) a(‘213’) = 231 = 45
a(40) a(‘220’) = 202 = 34
a(41) a(‘221’) = 212 = 38
a(42) a(‘222’) = 222 = 42
a(43) a(‘223’) = 232 = 46
a(44) a(‘230’) = 203 = 35
a(45) a(‘231’) = 213 = 39
a(46) a(‘232’) = 223 = 43
a(47) a(‘233’) = 233 = 47
a(48) a(‘300’) = 300 = 48
a(49) a(‘301’) = 310 = 52
a(50) a(‘302’) = 320 = 56
a(51) a(‘303’) = 330 = 60
a(52) a(‘310’) = 301 = 49
a(53) a(‘311’) = 311 = 53
a(54) a(‘312’) = 321 = 57
a(55) a(‘313’) = 331 = 61
a(56) a(‘320’) = 302 = 50
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