OFFSET
0,1
COMMENTS
In other words, this constant satisfies x = Sum_{n>=0} ( floor(10*n*x) (mod 10) ) / 10^n.
FORMULA
a(n) = floor(10*n*x) (mod 10), where x = Sum_{k>0} a(k)/10^k.
a(n) = 9 - A071873(n).
EXAMPLE
x = .49494949494949494948383838383838383838372727272727...
a(5) = 4 since floor(10*5*x) (mod 10) = 4.
The multiples of this constant x begin:
1*x = 0.4949494949494949494838383838383838383837...
2*x = 0.9898989898989898989676767676767676767675...
3*x = 1.484848484848484848451515151515151515151...
4*x = 1.979797979797979797935353535353535353535...
5*x = 2.474747474747474747419191919191919191919...
6*x = 2.969696969696969696903030303030303030302...
7*x = 3.464646464646464646386868686868686868686...
8*x = 3.959595959595959595870707070707070707070...
9*x = 4.454545454545454545354545454545454545454...
10*x = 4.949494949494949494838383838383838383837...
11*x = 5.444444444444444444322222222222222222221...
12*x = 5.939393939393939393806060606060606060605...
wherein the tenths place of n*x yields the n-th digit of x.
MATHEMATICA
k = 4; f[x_] := Floor[10*FractionalPart[x]]; Clear[xx]; xx[n_] := xx[n] = Catch[For[x = xx[n - 1], True, x += 10^(-n), If[f[n*x] == f[10^(n - 1)*x], Throw[x]]]]; xx[1] = k/10; Scan[xx, Range[100]]; RealDigits[xx[100]][[1]] (* Jean-François Alcover, Dec 06 2012 *)
Clear[a]; a[1] = 4; a[2] = 9; a[n0 = 3] = 4; a[_] = 0; digits = 10^(n0-1); Do[a[n] = Mod[Floor[10*n*Sum[a[k]/10^k, {k, 1, n}]], 10], {n, n0+1, digits}]; Table[a[n], {n, 1, digits}]
CROSSREFS
KEYWORD
AUTHOR
Paul D. Hanna, Jun 06 2002
STATUS
approved