A071793 Decimal expansion of the fifth (of 10) decimal selvage number; the n-th digit of a decimal selvage number, x, is equal to the tenths digit of n*x.

4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 9, 4

Offset

0,1

Comments

In other words, this constant satisfies x = Sum_{n>=0} ( floor(10*n*x) (mod 10) ) / 10^n.

Links

Table of n, a(n) for n=0..99.

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

Cf. A071789, A071790, A071791, A071792, A071873, A071874, A071875, A071876, A071877.

Sequence in context: A224299 A141653 A336051 * A010714 A284018 A089090

Adjacent sequences: A071790 A071791 A071792 * A071794 A071795 A071796

Keyword

nonn,cons,base,nice

Author

Paul D. Hanna, Jun 06 2002

Status

approved