A071874 Decimal expansion of the seventh (of 10) decimal selvage number; the n-th digit of a decimal selvage number, x, is equal to the tenths digit of n*x.

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

Offset

0,1

Comments

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

The seventh selvage number is equal to the complement of the fourth selvage number (A071792): s_7 = 1 - s_4.

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 - A071792(n).

Example

x=0.62851730629517406395184073952841739628517306295174...
a(7) = 3 since floor(10*(7*x)) (Mod 10) = 3.
The multiples of this constant x begin:
1*x = 0.6285173062951740639518407395284173962852...
2*x = 1.257034612590348127903681479056834792570...
3*x = 1.885551918885522191855522218585252188856...
4*x = 2.514069225180696255807362958113669585141...
5*x = 3.142586531475870319759203697642086981426...
6*x = 3.771103837771044383711044437170504377711...
7*x = 4.399621144066218447662885176698921773996...
8*x = 5.028138450361392511614725916227339170281...
9*x = 5.656655756656566575566566655755756566567...
10*x = 6.285173062951740639518407395284173962852...
11*x = 6.913690369246914703470248134812591359137...
12*x = 7.542207675542088767422088874341008755422...
wherein the tenths place of n*x yields the n-th digit of x.

Mathematica

k = 6; 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] = 6; a[2] = 2; a[n0=3] = 8; 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, A071875, A071876, A071877.

Sequence in context: A062771 A249919 A254868 * A011331 A155687 A021618

Adjacent sequences: A071871 A071872 A071873 * A071875 A071876 A071877

Keyword

cons,easy,nonn,base

Author

Paul D. Hanna, Jun 10 2002

Status

approved