A071873 Decimal expansion of the sixth (of 10) decimal selvage number; the n-th digit of a decimal selvage number, x, is equal to the tenths digit of n*x.

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

Offset

0,1

Comments

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

The sixth selvage number is equal to the complement of the fifth selvage number: s_6 = 1 - s_5.

Links

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

MathWorld, Equidistributed Sequence

Formula

a(n) = floor[10*(n*x)] (Mod 10), where x = sum{k=1..inf} a(k)/10^k.

a(n) = 9 - A071793(n).

Example

x=0.50505050505050505051616161616161616161627272727272...
a(7) = 5 since floor(10*(7*x)) (Mod 10) = 5.
The multiples of this constant x begin:
1*x = 0.5050505050505050505161616161616161616163...
2*x = 1.010101010101010101032323232323232323233...
3*x = 1.515151515151515151548484848484848484849...
4*x = 2.020202020202020202064646464646464646465...
5*x = 2.525252525252525252580808080808080808081...
6*x = 3.030303030303030303096969696969696969698...
7*x = 3.535353535353535353613131313131313131314...
8*x = 4.040404040404040404129292929292929292930...
9*x = 4.545454545454545454645454545454545454546...
10*x = 5.050505050505050505161616161616161616163...
11*x = 5.555555555555555555677777777777777777779...
12*x = 6.060606060606060606193939393939393939395...
wherein the tenths place of n*x yields the n-th digit of x.

Mathematica

k = 5; 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] = 5; a[2] = 0; a[n0=3] = 5; 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}] (* Jean-François Alcover, May 12 2015 *)

Crossrefs

Cf. A071789, A071790, A071791, A071792, A071793, A071874, A071875, A071876, A071877.

Cf. A257875 (continued fraction).

Sequence in context: A167260 A137520 A010676 * A036478 A059628 A325972

Adjacent sequences: A071870 A071871 A071872 * A071874 A071875 A071876

Keyword

cons,easy,nonn,base

Author

Paul D. Hanna, Jun 10 2002

Status

approved