A071877 Decimal expansion of the tenth (of 10) decimal selvage number; the n-th digit of a decimal selvage number, x, is equal to the tenths digit of n*x.

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

Offset

0,1

Comments

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

The tenth selvage number is equal to the complement of the first selvage number (A071789): s_10 = 1 - s_1.

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 - A071789(n).

Example

x=0.87653210876532109765421097654210986543109865431098...
a(7) = 1 since floor(10*(7*x)) (Mod 10) = 1.
The multiples of this constant x begin:
1*x = 0.8765321087653210976542109765421098654311...
2*x = 1.753064217530642195308421953084219730862...
3*x = 2.629596326295963292962632929626329596293...
4*x = 3.506128435061284390616843906168439461724...
5*x = 4.382660543826605488271054882710549327155...
6*x = 5.259192652591926585925265859252659192587...
7*x = 6.135724761357247683579476835794769058018...
8*x = 7.012256870122568781233687812336878923449...
9*x = 7.888788978887889878887898788878988788880...
10*x = 8.765321087653210976542109765421098654311...
11*x = 9.641853196418532074196320741963208519742...
12*x = 10.51838530518385317185053171850531838517...
wherein the tenths place of n*x yields the n-th digit of x.

Mathematica

k = 8; 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] = 8; a[2] = 7; a[n0=3] = 6; 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, A071792, A071873, A071874, A071875, A071876.

Sequence in context: A200598 A021846 A201579 * A138472 A022964 A023450

Adjacent sequences: A071874 A071875 A071876 * A071878 A071879 A071880

Keyword

cons,easy,nonn,base

Author

Paul D. Hanna, Jun 10 2002

Status

approved