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 A109865 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). 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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. LINKS Harvey P. Dale, Table of n, a(n) for n = 0..1000 MAPLE 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 MATHEMATICA First[#]&/@Module[{nn=110, pi}, {pi=RealDigits[Pi, 10, nn][[1]]}; NestList[ Abs[ Differences[ #]]&, pi, nn-1]] (* Harvey P. Dale, Jun 14 2016 *) CROSSREFS Cf. A000796. Sequence in context: A202820 A113081 A172184 * A206713 A096874 A090046 Adjacent sequences:  A109862 A109863 A109864 * A109866 A109867 A109868 KEYWORD base,nonn AUTHOR Amarnath Murthy, Jul 09 2005 EXTENSIONS More terms from R. J. Mathar, Feb 11 2008 Definition clarified by Harvey P. Dale, Jun 14 2016 STATUS approved

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Last modified August 17 21:47 EDT 2022. Contains 356189 sequences. (Running on oeis4.)