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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).

%I A109865 #16 Jun 14 2016 16:17:53
%S A109865 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,
%T A109865 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,
%U A109865 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
%N 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).
%C A109865 3...1...4...1...5...9...2...6...5...3...5...8...9...7...9...3...2...3...8...4
%C A109865 ..2...3...3...4...4...7...4...1...2...2...3...1...2...2...6...1...1...5...4
%C A109865 ....1...0...1...0...3...3...3...1...0...1...2...1...0...4...5...0...4...1
%C A109865 ......1...1...1...3...0...0...2...1...1...1...1...1...4...1...5...4...3
%C A109865 ........0...0...2...3...0...2...1...0...0...0...0...3...3...4...1...1
%C A109865 ..........0...2...1...3...2...1...1...0...0...0...3...0...1...3...0
%C A109865 ............2...1...2...1...1...0...1...0...0...3...3...1...2...3
%C A109865 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.
%H A109865 Harvey P. Dale, <a href="/A109865/b109865.txt">Table of n, a(n) for n = 0..1000</a>
%p A109865 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
%t A109865 First[#]&/@Module[{nn=110,pi},{pi=RealDigits[Pi,10,nn][[1]]};NestList[ Abs[ Differences[ #]]&,pi,nn-1]] (* _Harvey P. Dale_, Jun 14 2016 *)
%Y A109865 Cf. A000796.
%K A109865 base,nonn
%O A109865 0,1
%A A109865 _Amarnath Murthy_, Jul 09 2005
%E A109865 More terms from _R. J. Mathar_, Feb 11 2008
%E A109865 Definition clarified by _Harvey P. Dale_, Jun 14 2016