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

Author

Amarnath Murthy, Jul 09 2005

Keywords

• base
• nonn

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

Crossrefs

Cf. A000796.

Programs

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 *)

Extensions

More terms from R. J. Mathar, Feb 11 2008

Definition clarified by Harvey P. Dale, Jun 14 2016