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A124793
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Numbers in a perpendicular plane intersecting a 3D clockwise spiral produced by powers of 2.
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1
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1, 5, 35, 157, 1123, 5021, 35939, 160669, 1150051, 5141405, 36801635, 164524957, 1177652323, 5264798621, 37684874339, 168473555869, 1205915978851, 5391153787805, 38589311323235, 172516921209757, 1234857962343523
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The general formula for powers of k integer is a(n)=k^{1/4*[10*n-7-(-1)^n]}+k^{1/4*[10*n-1+(-1)^n]}-a(n-1), with a(0)=1 and where k is an integer value. If we replace k with "i" or "-i", being i=sqrt(-1), we get a periodic complex sequence (period 8).
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LINKS
| Charles R Greathouse IV, Table of n, a(n) for n = 1..1329
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FORMULA
| a(n)=2^{1/4*[10*n-7-(-1)^n]}+2^{1/4*[10*n-1+(-1)^n]}-a(n-1), with a(0)=1.
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EXAMPLE
| Write powers of 2 in a sort of 3D clockwise spiral. After the initial 1 (2^0) move right till 2^1=2 (pratically only one step); then move down till 2^2=4 (3,4); then left till 2^3=8 (5,6,7,8). When writing number 5 we are in the same column of 1 so 5 is the second number of the sequence. Then move up till 2^4=16. Then move up perpendicularly to the plane till 2^5=32 and again right till 2^6=64. The number 35 is in the sequence because lays in the same line of 1 and 5. The process continue down, left, up, perpendicular, right and so on.
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MAPLE
| P:=proc(n) local a, i, x, y; a:=1; print(a); for i from 1 by 1 to n do x:=1/4*(10*i-7-(-1)^i); y:=1/4*(10*i-1+(-1)^i); a:=2^x+2^y-a; print(a); od; end: P(100);
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CROSSREFS
| Cf. A108981, A001107.
Sequence in context: A005562 A097872 A184707 * A048515 A100739 A043014
Adjacent sequences: A124790 A124791 A124792 * A124794 A124795 A124796
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KEYWORD
| easy,nonn
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AUTHOR
| Paolo P. Lava & Giorgio Balzarotti (paoloplava(AT)gmail.com), Jun 27 2007
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