|
| |
|
|
A109865
|
|
Consider pi = 3.1415926535897932384626433832795... On taking the absolute difference between successive digits ignoring the decimal point one gets the following array. Sequence contains the first term of each row (the first diagonal).
|
|
0
| |
|
|
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; 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.
|
|
|
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 (mathar(AT)strw.leidenuniv.nl), Feb 11 2008
|
|
|
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 (amarnath_murthy(AT)yahoo.com), Jul 09 2005
|
|
|
EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 11 2008
|
| |
|
|
