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A109865
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Consider Pi = 3.1415926535897932384626433832795... On taking the absolute successive differences between successive digits ignoring the decimal point one gets the array shown in Comments (below). Sequence contains the first term of each row (the first diagonal).
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1
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3, 2, 1, 1, 0, 0, 2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0
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OFFSET
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0,1
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COMMENTS
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3...1...4...1...5...9...2...6...5...3...5...8...9...7...9...3...2...3...8...4
..2...3...3...4...4...7...4...1...2...2...3...1...2...2...6...1...1...5...4
....1...0...1...0...3...3...3...1...0...1...2...1...0...4...5...0...4...1
......1...1...1...3...0...0...2...1...1...1...1...1...4...1...5...4...3
........0...0...2...3...0...2...1...0...0...0...0...3...3...4...1...1
..........0...2...1...3...2...1...1...0...0...0...3...0...1...3...0
............2...1...2...1...1...0...1...0...0...3...3...1...2...3
Call this the Absolute Successive Difference function of an irrational number k denoted by ASDE(k). Then ASDE(Pi) = 3.211002110001... Subsidiary sequences: For e, phi, 2^(1/2), 3^(1/2), Euler's constant and other important irrational numbers can be included.
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LINKS
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MAPLE
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Digits := 200: asde := proc(n, L) local b, L2, i, j; b := L ; for i from 1 to n do L2 := [] ; for j from 1 to nops(b)-1 do L2 := [op(L2), abs(op(j+1, b)-op(j, b))] ; od: b := L2 ; od: op(1, b) ; end: A109864 := proc(n) local piL, i ; piL := [] ; for i from 1 to n+1 do piL := [op(piL), floor(Pi*10^(i-1)) mod 10] ; od: asde(n, piL) ; end: seq( A109864(n), n=0..100) ; # R. J. Mathar, Feb 11 2008
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MATHEMATICA
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First[#]&/@Module[{nn=110, pi}, {pi=RealDigits[Pi, 10, nn][[1]]}; NestList[ Abs[ Differences[ #]]&, pi, nn-1]] (* Harvey P. Dale, Jun 14 2016 *)
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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