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).

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

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